Session GP01 - Poster Session II.
POSTER session, Monday afternoon, March 22
Exhibit Hall, GWCC

[GP01.01] Collisional Properties of Ultracold Potassium: Consequences for Degenerate Bose and Fermi Gases

The hyperfine-state-selected scattering properties of potassium atoms at ultralow temperatures are calculated using accurate potentials gleaned from a recent analysis of photoassociation data. We predict that ^39K will possess a small, probably negative scattering length, which will hinder its evaporative cooling to the quantum degenerate regime, unless experiments take advantage of its magnetic-field-induced Feshbach resonance. The large, positive value calculated for the ^41K triplet scattering length makes it a better candidate for condensation at zero magnetic field. We also predict large, positive scattering lengths for experimentally relevant mixtures of spin states in the fermionic isotope ^40K. This result points to the likely possibility that ^40K may also be amenable to evaporative cooling. Moreover, certain spin states of ^40K also possess Feshbach resonances that may facilitate the creation of Cooper pairs in these gases. This work was supported in part by the National Science Foundation.

[GP01.02] Determination of ^39K Scattering Lengths Using Photoassociation Spectroscopy

Scattering lengths play an important role in the rapidly growing field of Bose-Einstein condensation in dilute atomic gases. To date, the scattering lengths are known quite accurately for Li, Na, Rb, and to a lesser extent Cs primarily through the analyisis of photoassociation experiments. We present the first theoretical analysis of the ^39K 0_g^- ro-vibrational spectrum which probes, via the free-bound Franck-Condon factors, the region of internuclear separation (R=40-80 a.u.) essential for determining the two-body scattering length a. Based on our fits of the spectral lineshapes and relative intensities we can restrict the bounds on the singlet and triplet scattering lengths to a_s = 138\pm 5 a.u. and a_t = -15\pm 30 a.u., respectively. In addition, the analyis incorporates the multichannel quantum defect ideas presented in Burke et. al, Phys. Rev. Lett. 81, 3355 (1998) dramatically increasing the effeciency of the calculations.

This work was supported in part by the National Science Foundation.

[GP01.03] Double-Resonance Photoassociative Spectroscopy of Ultracold ^39K Atoms near the Lowest Asymptote

We describe high resolution long-range molecular spectroscopy of ^39K_2 near the lowest 4^2S_1/2+4^2S_1/2 asymptote by \Lambda-type free-bound-bound double-resonance photoassociation of ultracold ^39K atoms. Hyperfine coupled bound levels within 5 GHz of the F''=1 + F''=1 threshold are observed in trap loss spectra via the pure long-range 0_g^- (v'=0, J'=2, R_c=52.2 a_0) intermediate state which dissociates to the 4^2S_1/2 + 4^2P_3/2 atomic limit. The binding energies of the near-threshold ground-state molecular levels allow accurate determination of the cold collision properties of potassium atoms, in particular the ground singlet and triplet scattering lengths. The triplet scattering length appears to be small and negative.

[GP01.04] What the Hamiltonian Structure of Ground State Alkali Atoms Tell us about K

An understanding of the Hamiltonian structure for two colliding ground state alkali atoms and the relationship between this structure and the singlet a_S and triplet a_T scattering lengths provided by nature is useful in interpreting experimental data based on cold collisions or photoassociation spectroscopy. As an example we will show how this information has been used in analyzing the experimental photoassociation spectra of the pure long-range ^39\rmK 1_u state in order to obtain a scattering lengths for K.

[GP01.05] Experimental study of ultra-cold metastable neon collisions

The odds for producing a Bose-Einstein condensate of metastable rare gas atoms depend to a large degree on (a) the sign and magnitude of the scattering length and (b) the rate of ionization in spin-polarized binary collisions at low temperatures (1). We have started an experimental program to try to determine these quantities for metastable neon by studying collisions in an atomic beam. Laser cooling is used to produce a sufficiently dense (>10^9/cm^3) and cold (<25mK) beam of metastable atoms for such studies (2). Ionization rates are determined with and without optical pumping into a spin-polarized state. Information about ground state potentials can be inferred from photoassociation spectroscopy. We hope to present our first experimental results at the conference. (1) M.R.\ Doery et al., Phys.\ Rev.\ A 58 (1998) 3673 (2) Details of the setup are shown on our web-site

[GP01.06] Observation of the Photoassociation Spectrum of Cold Cesium Atoms

Photoassociation spectra have been extensively studied in laser-cooled alkali atoms such as lithium, sodium, and rubidium. Analysis of these spectra yield important parameters such as the scattering length for cold collisions and precise determination of the lifetime of the upper atomic state for the relevant transition. Recent experiments have begun to study cesium atom photoassociation near the D2 (852 nm) transition(Fioretti, et. al.), Phys. Rev. Lett. 80, 4402 (1998).^,(Takekoshi, et. al.), to appear in Phys. Rev. A 59 (1999).. In this paper, we present photoassociation spectra obtained near the D1 (895 nm) transition in cesium. Laser-cooled and trapped Cs atoms are photoassociated using light from a tunable Ti:Sapphire laser near 895 nm. The Ti:Sapphire laser is mixed with light from a diode laser locked to the D1 atomic transition so that the absolute frequency of the light can be determined using a heterodyne technique. Further analysis of this data will increase the accuracy of the scattering length and atomic excited state lifetime for Cs.

[GP01.07] Ultracold atom-ion collisions: the case of Na+Na^+

Studies of charge exchange and total cross sections in elastic collisions of atom-ion alkali metals at ultralow temperatures are reported. Calculations for Na+Na^+ have been carried out with the best available ^2\Sigma_g and ^2\Sigma_u potential curves. As functions of energy, the cross sections show considerable structure and are large in the limit of low temperature. The scattering lengths were also computed, and the effective range expansion verified. For higher temperatures, we compare quantal and semi-classical results, and investigate the range of applicability of the Langevin formula. Even at temperatures of few degrees Kelvin, the charge exchange cross sections are large, and could provide an efficient way to produce cold ions.

[GP01.08] Analytical wavefunctions for ultracold H + H collisions

Exact wavefunctions describing molecular dissociation at large internuclear separations are utilized to calculate the scattering cross section of two hydrogen atoms at ultracold temperatures. The scattering calculations are performed by numerically integrating Schroedinger's equation over short distances, and matching the solutions onto analytical wavefunctions describing the relative motion of distant atoms. Accurate potentials are used in the short-range region, while the long-range solutions depend soley on well-known dispersion coefficients and the reduced mass of the two-atom system.

[GP01.09] High-precision calculations of van der Waals coefficients, polarizabilities, and atom-wall interaction coefficients for alkali-metal atoms.

The van der Waals interaction plays an important role in characterizing the ultra-cold temperature collisions between two ground state alkali-metal atoms and accurate knowledge of its value can impact predictions of whether a Bose-Einstein condensate is stable for a particular system. Other experiments are yielding constraints on magnitudes of the coefficients. We present results for C_6 dispersion coefficients, static dipole polarizabilities, and atom-wall interaction coefficients based on ab initio calculations of frequency-dependent dipole polarizabilities. We combine several many-body techniques to calculate various contributions to the polarizability. In particular, we used a linearized coupled-cluster method truncated at the level of single and double excitations to obtain the leading contribution from valence states. The contribution from autoionizing states which enters through the core polarizability is obtained within the framework of the relativistic random-phase approximation.

[GP01.10] Energy Transfer Collisions in a Sample of Cold Rydberg Atoms

In the last few years the idea of using trapped neutral atoms to produce cold Rydberg atoms has drawn special attention. With the advent of the MOT cold samples of Rydberg atoms, which are naturally Doppler-free, can now be produced. This achievement opens a complete new possibilities to study collisions involving Rydberg atoms. In this work we study the energy transfer collision process involving the 28P, 28S, and 29S excited states in cold Rubidium. The time evolution of the 29 S state population is followed by field ionization. Our setup is constituted by a standard Rubidium vapor cell MOT, using stabilized diode lasers for the trapping and repumping laser beams. A pulsed laser was used to excite the Rydberg atoms. The cold cloud of atoms is formed between two metal grids, separated by 2 cm from each other. In one of them we apply a fast HV pulse in order to ionize the Rydberg atoms. The ions are detected by a channeltron particle multiplier. By varying the delay between the light pulse and the HV pulse we can monitor the 29S population. A model based on rate equations, which takes in account radiative decays and energy transfer collisions, agrees well with the experiment results. Work supported by FAPESP and Programa Pronex.

[GP01.11] Quasiresonant energy transfer in ultracold atom-diatom collisions

We investigate ultracold He--H_2 collisions, and find that they are dominated by quasiresonant vibration-rotation energy transfer. Classical trajectory computations show that extremely strong correlations between \Delta j and \Delta v persist at low energies, leaving an adiabatic constant of the motion that is conserved to better than one part in 10^5. However, the classically allowed changes to j and v are substantially less than one quantum, so state-to-state transitions are classically forbidden. Quantum reaction rate computations show that quasiresonant transitions occur in the limit of zero collision energy, but that threshold effects become important and that some quasiresonant channels close. The qualitative similarity between classical and quantum results suggests that they share a common mechanism.

[GP01.12] The repulsive 1/r^3 interaction

Analytic solutions of the Schrödinger equation are presented for a repulsive 1/r^3 potential. They lead to an in-depth understanding of scattering by a pure repulsive 1/r^3 interaction including exact cross sections and phase shifts. Scattering by any potential which is asymptotically a repulsive 1/r^3 is also discussed. The results have applications in cold-atom collisions in a laser field and in many other quantum systems where the repulsive 1/r^3 interaction can be due to resonant electric dipole-dipole, magnetic dipole-dipole, or quadrupole-monopole interactions.

[GP01.13] Accuracy of Close-Coupling approaches using Single-Center Expansions for Positron-Atom Scattering

For positron-atom scattering, the break-up channel contains both the effects of ionization and positronium formation. In a single-center close-coupling expansion, these effects must be contained in the bound and continuum states. In previous R-matrix calculations for positron-lithium scattering, it was found that that the cross sections for exciting the 3d state were anomalously large and it has been argued that the atomic d-states try to represent the positronium formation channels and in so doing over estimate the cross sections for excitation to this state. It has further been argued that the only way to avoid this problem is to use a two center basis set expansion. We have investigated this hypothesis using a single-center convergent-close-coupling (CCC) method and have found that accurate N=2 and N=3 cross sections can be obtained using a single-center expansion even for energies just above the ionization threshold.

[GP01.14] Electron Attachment and Detachment: COT

Electron attachment to cyclooctatetraene (C_8H_8) has been studied over the temperature range 297-389 K using a flowing-afterglow Langmuir-probe apparatus. COT was chosen for study because recent experiments showed a large conformal change between the negative ion and neutral.^1 Photodetachment of the planar negative ion leads to a planar transition state for ring inversion in tub-like neutral COT. The question is, how does this unusual conformal change affect electron attachment? The rate constant for electron attachment (297-389 K) is 3.7 x 10^-9 cm^3/s (about 1 attachment in 100 collisions). The electron affinity of COT is low enough that thermal electron detachment takes place in our temperature range, and detachment rates have been measured; the activation energy for detachment is 190 meV. The electron affinity of COT may be deduced from the equilibrium constant (0.59 eV) and will be compared to the results of other work. 1. P.G. Wenthold, D.A. Hrovat, W.T. Borden, and W.C. Lineberger, Science 272, 1456-1459, 1996.

[GP01.15] Electron Excitation at Forward Scattering.^1

The Regge pole representation of scattering problems embodies deep physical insights [1] and is not a merely contrived mathematical convinience. No physical understanding of angular distributions of a molecular collision process is achieved through summing a partial wave series with significant terms [2]. At forward scattering, the recent generalized Lassettre expansion [3], the momentum dispersion method [4] and the forward scattering function [5] all yield results for H~1s--2p excitation that agree excellently with those obtained by the convergent close--coupling approximation [6] down to about twice threshold energy. Measured electron DCS_s for Cd and Xe are used to demonstrate the utility of the analytical continuation of the measured data in angle and energy. This should encourage experimenters to measure in the difficult to access angular regime near and at \theta =0^\circ. \vglue .1in ^1Supported by NSF and DOE Division of Chemical Siences, Office of Basic Energy Sciences, Office of Energy Research. \vglue .1in \begintabularll [1]& J. N. L. Connor, J.~Chem. Soc. Farad. Trans. 86, 1627(1990) [2] &D. Sokolovski et.~al., Chem. Phys. Lett. 238, 127(1995) [3] &Z. Felfli et.~al., Phys. Rev. Lett. 81, 963(1998) [4] &A. Haffad et.~al., Phys. Rev. Lett. 76, 2456(1996) [5] &N. Avdonina et.~al., J. Phys. B 30, 2591(1997) [6] &I. Bray et.~al., Phys. Rev. A 44, 5586(1991) \endtabular

[GP01.16] Measurement of the electron--impact excitation cross sections for n = 1 \rightarrow 2 transitions in heliumlike and hydrogenlike xenon

Electron--impact excitation cross sections are important parameters for modeling energy transport mechanisms and are crucial for developing accurate spectral diagnostics in high--temperature plasmas. At the Livermore high--energy electron--beam--ion--trap facility (SuperEBIT) the K\alpha transitions in heliumlike Xe^52+ and hydrogenlike Xe^53+ have been measured using a transmission--type crystal spectrometer. The spectral resolution is sufficient to resolve the fine structure of the xenon K\alpha spectrum and, thus, to perform level--specific measurements of the electron--impact excitation cross sections. In particular, the determination of the cross sections includes the 1s^2\, 1\! S_0 \rightarrow 1s2p^\, 1\! P_1 , 1s^2\, 1\! S_0 \rightarrow 1s2p^\, 3\! P_1 , and 1s^2\, 1\! S_0 \rightarrow 1s2s^\, 3\! S_1 transitions in heliumlike Xe^52+ and the 1s_1/2 \rightarrow 2p_3/2 , and 1s_1/2 \rightarrow 2p_1/2 transitions in hydrogenlike Xe^53+. The uncertainties of the measured cross sections are in the 10%\ range and are mainly due to low counting statistics. Comparison with theoretically predicted values shows that agreement between the measured and calculated values can only be found when the Breit interaction is included in the calculations.

[GP01.17] Electronic excitation of hydrocarbons: Methylene and Ethylene

Electron collisions with polyatomic systems within the R-matrix methodology (L. A. Morgan, J. Tennyson and C. J. Gillan Comp. Phys. Commun. 114) 120 (1998). (L. A. Morgan, and J. Tennyson Phil Trans. B in press) (1998). is currently being undertaken as part of a UK wide collaborative project based on the SWEDEN-MOLECULE Gaussian code. Data on electron collisions with various hydrocarbons are required for many practical purposes such as plasma chemical processing and deposition, gas laser modeling, astrophysical processes, atmospheric modeling and for fundamental spectroscopic purposes. The present work concentrates on electron collisional excitation for the methylene radical (CH_2) and the ethylene (C_2H_4) complex. A multi--state CI approximation is used for both polyatomic systems where the lowest three target states are included in the CI expansions using pseudo-natural orbitals. Our calculations allow comparisons to be made directly with existing ab initio work performed using the Schwinger and Kohn methods and with the available experimental data. Detailed cross section comparisons will be made and a comprehensive set of results will be presented at the meeting.

[GP01.18] Electron collisional excitation of doubly ionized Neon

Observations on the spectra of doubly ionized neon (NeIII) have been recently recorded below 25O Å(A. E. Livington, R. Buttner, A. S. Zacarias, B. Kraus, K-H Schartner, F. Folkmann and P. H. Mokler, J. Opt. Soc. Am. B 14) 522-525 (1997).. This work together with previous studies give line intensies which may be used as density diagnostics but required accurate collision strengths and transition probabilities for their interpretation. We are currently undertaking detailed calculations for electron collisions with NeIII ions performed using the R-matrix method within the Breit-Pauli approximation. Multi-state configuration interactions wave functions incorporating the lowest lying twenty eight LS-coupled target states of NeIII are used in our work. Calculations for cross sections and rates are in progress and a comparison will be made with previous work which included only four LS-coupled states of NeIII (K.Butler and C. Mendoza, Mon. Not. R. Astr. Soc. 208) 17-23 (1984).. Further details and results will be presented at the meeting.

[GP01.19] Effective collision strengths for fine-structure forbidden transitions among the 3s^23p^3 levels of Cl~III

Electron temperatures and densities are difficult to determine in many astrophysical plasmas. However, it is well known that diagnostics on forbidden line intensity ratios for ions in the phosphorous isoelectronic sequence are of great importance in astrophysics, particularly for nebulae. A key element in the analysis is highly accurate atomic data. In this work we extend the earlier calculations of Butler and Zeippen (Astron. Astrophys. 208 337 (1989)) on electron scattering by Cl~III. We have obtained effective collision strengths for a wide range of electron temperatures using the R-matrix method. Twenty-three LS target eigenstates are included in the expansion of the total wavefunction, consisting of the seven n=3 states with configuration 3s^23p^3 and 3s3p^4, twelve n=3 states with configuration 3s^23p^23d, and four n=4 states with configuration 3s^23p^24s. The fine-structure collision strengths have been obtained by transforming to a jj-coupling scheme using the JAJOM program of Saraph (Comp. Phys. Commun. 15 247 (1978)) and have been determined at a sufficiently fine energy mesh to delineate properly the resonance structure. Results for both collision strengths and for effective collision strengths will be presented at the conference and comparison will be made with the earlier work.

[GP01.20] Simultaneous Electron-Impact Ionization--Excitation of Quasi-Two-Electron Atoms.

The general R-matrix code for electron-impact ionization~[1] has been modified (i)~to allow for high incident electron energies within the Plane-Wave Born Approximation (PWBA) and (ii)~to improve upon the description of both the target ground state and the interaction of the ejected electron with the residual ion via an R-matrix with pseudo-states (RMPS) approach~[2]. Results for cross sections (total, \hboxsingle-, \hboxdouble-, and triple-differential) as well as parameters measured in electron--photon coincidence experiments~[3] for ionization resulting in excited ionic states will be presented and compared with experimental data and predictions from other theoretical approaches. \par\medskip 1. K.~Bartschat, Comp.~Phys.~Commun.~75, 219 (1993) 2. K.~Bartschat, Comp.~Phys.~Commun.~114, 168 (1998) 3. M.~Dogan et al., J.~Phys.~B~31, 1611 (1998)

[GP01.21] (e,2e) Studies of Helium Autoionizing Levels

The helium 2\ell2\ell' autoionizing region is being investigated using (e,2e) spectroscopy. The present experiments are similar in concept to recent (e,2e) experiments in cadmium.(N.L.S. Martin, D.B. Thompson, R.P. Bauman and M. Wilson, Phys.\ Rev.\ A 50), 3878 (1994). Pairs of (e,2e) energy spectra for a given incident energy and scattering angle are taken at ejected-electron directions 180^\circ apart. The sum and difference of such spectra give information about interference cross-terms between different multipole partial wave amplitudes. Experiments are being carried out for incident electron energies of up to 500~eV.

[GP01.22] Electron-Impact Excitation of Neon from both the ground level and metastable levels

Knowledge of electron-impact excitation cross sections from both the ground state and metastable levels of atoms is needed for both a comprehensive understanding of the electron excitation process and the modeling of plasmas and discharges. We have previously studied excitation into the ten levels of the 3p^54p configuration of argon from both the ground level,(J. E. Chilton et al.), Phys. Rev. A 57, 267 (1998). and metastable levels.(G.A. Piech et al.), Phys. Rev. Lett. 81, 309 (1998). We are now in the process of studying the analogous excitation cross sections in neon. In contrast to argon, the pressure effects in the ground state excitation cross sections are much less. The cross sections for excitation processes out of the 1s_5 (^3P_2) metastable level of neon corresponding to optically allowed transitions (into 2p^53p levels with J=1,2,3) are very large with a broad dependence on the incident electron energy- similar to what we have found for argon.

[GP01.23] Use of Trapped Rb Atoms as a Target for Measurements of Electron-Impact Cross Sections

Trapped atoms are a unique target for measuring cross sections for electron-impact ionization and excitation.(R. S. Schappe et al.), Phys. Rev. Lett. 76, 4328 (1996). A special property of atom traps, which we now wish to exploit, is that a substantial fraction of the atoms are pumped into the 5^2P_3/2 excited level by the trapping radiation. Thus it is possible to obtain cross sections out of both the 5^2S ground level and the 5^2P excited level by comparing the signals obtained with the trapping laser on (5^2S and 5^2P) and with the lasers momentarily turned off (5^2S alone). We are presently working on determining the ionization cross section out the Rb(5^2P_3/2) excited level by measuring the subsequent change in the trap loss rate. We are also developing a newer trapping apparatus to measure excitation cross sections by detecting the fluorescence given off by electron-impact excited atoms. Preliminary results for Rb(5^2S \rightarrow 5^2P) excitation will be presented.

[GP01.24] Measurement of electron excitation cross sections of the 3p^54p, 3p^53d, 3p^55s levels of argon using Fourier transform spectrometry

Advances in Fourier transform spectrometers (FTS) allow previously unexamined excited levels of argon to be studied through detection of their infrared (1 - 6 \mu m) emissions. We find that radiation from the 3p^54p levels excited by an electron beam exhibits nonlinear dependence on gas pressure. We attribute this to the reabsorption of resonant photons by higher levels coupled to both the ground and the 3p^54p levels. We measure infrared transitions from the dominant 3p^55s and 3p^53d cascading levels, which display similar pressure effects. Subtraction of these cascade processes from the observed 3p^54p \rightarrow 3p^54s signals yields the direct electron excitation cross sections for the 3p^54p levels, which remain independent of gas pressure. The prominent cascades into the 3p^55s and 3p^53d levels can also be studied with the FTS, and the direct electron excitation cross sections extracted. We present direct cross sections for all 3p^54p levels, and the J = 0, 2, 3, 4 3p^55s and 3p^53d levels. Apparent cross section data at various energies and gas pressures are also presented.

[GP01.25] Absolute partial cross sections for electron-impact ionization of CO from threshold to 1000 eV

Absolute partial cross sections for the production of both parent and fragment ions from electron-impact ionization of CO are reported for electron energies from threshold to 1000 eV. The product ions are mass analyzed using a time-of-flight mass spectrometer and detected using a position-sensitive detector whose output demonstrates that all product ions are completely collected. The overall uncertainty in the absolute cross section values for singly charged parent ions is \pm4% and is slightly greater for fragment ions. Previous cross section measurements are compared to the present results.

[GP01.26] Electron Impact Excitation to and from the Metastable States of Kr I

Electron impact excitation rates to and from the metastable levels of noble gases such as argon, krypton, and xenon are essential inputs to interpreting rare gas actinometry as a diagnostic of molecular dissociation in plasma processing applications. These rates are also important for spectral analysis of lighting discharges and modeling of excimer laser amplifiers. We have already calculated the excitation cross sections to and from the metastable levels of argon using a distorted-wave method and find very large cross sections from the metastable levels. These cross sections will thus significantly affect the level populations of the metastables for any diagnostics. We present similar calculations of excitation cross sections from the ground and metastable levels for neutral krypton using DW method and including polarization for incident electron energies up to 100 eV. Unlike the argon case, there exist relatively little experimental data or theoretical calculations for electron impact excitation of neutral krypton. We will compare and contrast our results with those available at present.

[GP01.27] Inelastic Scattering of Electrons from Singly-Ionized Oxygen

Cross sections for the electron impact excitation of the ground 2s^22p^3~^4S^o state to the 2s^22p^3~^2D^o, ^2P^o, and 2s2p^4~^4P states of singly-ionized oxygen are computed in a 28-state close coupling approximation using the R-matrix method. Extensive configuration interaction wave functions are used to represent twenty eight LS states of the 2s^22p^3, 2s2p^4, 2s^22p^23s, 2s^22p^23p, 2s^22p^23d, and 2s^22p^24s configurations of O II. These wave functions are also used to calculate excitation energies, oscillator strengths of electric-dipole-allowed transitions among various states, and radiative lifetimes of excited states. The calculated excitation energies are in close agreement with recent laboratory measurement. Our calculated oscillator strengths, lifetimes, and cross sections will be compared with other calculations and experiments.

[GP01.28] Cross Sections for the Scattering of Electrons by Atomic Nitrogen

R-matrix method is used to calculate the differential and integral cross sections of the forbidden 2s^22p^3~^4S^o - 2s^22p^3~^2D^o transition for the scattering of electrons from atomic nitrogen in a 11-state close-coupling approximation. Extensive configuration interaction wave functions are used to represent target states which give excitation energies in close agreement with experiment. The calculated differential cross sections are peaked in the backward direction and compare very well with the recent measurement. The integral cross sections show very good agreement with the available other calculations and measurement.

[GP01.29] Heteronuclear hydrogen molecular ion: revisited

We revisit a fundamental and familiar problem in molecular spectroscopy, HD^+. Unlike its brethren, H^+_2 and D_2^+ whose Born-Oppenheimer (BO) Hamiltonian separates in prolate-spheroidal coordinates thereby preserving the symmetry under exchange of the nuclei, the physics of HD^+ is profoundly different. Owing to the mass difference between the proton and deuteron, the symmetry under the exchange of the nuclei is broken, and the adiabatic potential energy curves now nearly cross within each molecular symmetry and give rise to non-adiabatic transitions. A far more profound influence of this mass difference is that because the geometric center and the nuclear center of mass do not coincide, a permanent electric dipole is formed in the ground and excited electronic states. Historical developments in theoretical treatment of HD^+ have begun with a body-fixed coordinate system with the origin placed at the geometric center of the nuclei. H_2^+ electronic wavefunctions are used at a later stage to obtain the eigenvalues of the symmetry-breaking operator. We begin with a treatment of the BO Hamiltonian in the center of mass of the nuclei and rewrite the Hamiltonian in prolate-spheroidal coordinates with the origin at the center of mass. In this fashion, we explicitly include information about the reduced nuclear mass in the BO adiabatic Hamiltonian. The adiabatic potential energy curves which we obtain give the correct dissociation thresholds. We present precise calculations of the HD^+ potential energy curves, coupling matrix elements, transition dipole matrix elements, varational energies and transition frequencies. We are motivated by a need for spectroscopic accuracy. We are also motivated to investigate effects beyond the adiabatic approximation for which we can calculate accurate coupling matrix elements.

[GP01.30] A Full Quantum-Mechanical Calculation Involving Low-Rydberg Alkali Atoms

To assess the reliability and limitation of the semi-classical Molecular Orbital approximation for estimating the depopulation cross sections of low-Rydberg alkali atoms in the thermal energy region, a 2-channel full quantum-mechanical calculation on these atoms colliding with the ground state He has been reported. A comparative study between the results reveals that the semi-classical approach is reliable and accurate for v > 5 x 10^-4 a. u.. Extreme low-energy results are found sensitive to various quantal effects.

[GP01.31] Status of 2s^2p-2s2p^2-2p^3 transition probabilities in B-like ions: theory and experiment

Transition probabilities are calculated for 49 electric dipole 2s^22p--2s2p^2--2p^3 transitions in boronlike ions with nuclear charges ranging from Z=5 to 100. Relativistic many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations are carried out with two potentials: a non-local 1s^2 Dirac-Fock potential and a local 1s^2 model potential. We use first-order perturbation theory to obtain intermediate coupling coefficients, and the second-order MBPT to determine the matrix elements. The contributions from negative-energy states are included in the second order E1 matrix elements to achieve precise agreement between length-form and velocity-form amplitudes. The transition energies used in the calculation of oscillator strengths and transition rates are obtained from second-order MBPT. Transition probabilities are compared with critically evaluated experimental values and with results from other recent calculations.

[GP01.32] Relativistic many-body calculations of energy levels, hyperfine constants, and dipole matrix elements for alkali metal atoms.

We calculate removal energies and hyperfine constants for ns, np_1/2 and np_3/2 states of Na (n=3,4,5,6,7), K (n=4,5,6,7), Rb (n=5,6,7,8) and Cs (n=6,7,8,9). We also calculate removal energies for the ground state and several excited states of Fr. The calculations are carried out using relativistic all-order method including single, double and partial triple excitations of the Hartree-Fock ground state (SDpT). We use the SDpT wave functions to evaluate electric-dipole (E1) reduced matrix elements for transition between these states. We found that single-double approximation gives accurate results for removal energies and dipole matrix elements for the principal transition. The hyperfine constants for ^23Na, ^39K, ^85Rb, ^133Cs are found to be in good agreement with experiment after triple excitations are partially included. These calculations provide a basis for evaluation of PNC amplitudes in Cs and Fr.

[GP01.33] Strong Electric-field Effects on the Structure Profiles of Doubly Excited Resonances in He Ground State Photoionization

Electric-field effects on the doubly excited resonance structures in He ground state photoionization are investigated theoretically using the complex-rotation method(Y.K. Ho, Phys. Rep. 99), 1 (1983); A. Buchleitner, B. Gremaud, and D. Delande, J. Phys. B 27, 2663 (1994). with B-spline-based basis(T.N. Chang, in Many-body Theory of Atomic Structure and Photoionization), edited by T.N. Chang (World Scientific, Singapore, 1993), p.213.. States up to L_max=3 are coupled together by the external electric field for both initial and final states. The variations of the resonance structure profiles and Fano q-parameters for the M=0 components of He (2,na) (n=2-5) ^1P^o and ^1D^e doubly excited resonances series for selected DC electric field strengths are examined. The change of the resonance energies and widths will also be presented.

[GP01.34] Determination of Resonance Energies and Widths of Mg Doubly Excited States above the 3s and/or 3p Thresholds by the Stabilization Method with the B-spline-based Configuration Interaction Approach

The resonance energies and widths of Mg ^1P^o, ^1D^e, and ^1F^o doubly excited states above the 3s and/or 3p thresholds are determined by calculating the density of resonance states using the stabilization method(V.A. Mandelshtam, T.R. Ravuri, and H.S. Taylor, Phys. Rev. Lett. 70), 1932 (1993). with the B-spline-based configuration interaction (BSCI) approach(T.N. Chang, in Many-body Theory of Atomic Structure and Photoionization), edited by T.N. Chang (World Scientific, Singapore, 1993), p.213.. The effects due to the intrashell core excitation and intershell core-valence interactions are taken into account in the BSCI calculations by using a parametrized long-range core-polarization potential. The procedure of extracting the resonance energies and widths from the stabilization diagram, and comparisons with other results in the literature will be presented.

[GP01.35] Electron Affinity of He^- 1s2s\,^3S

In Kristensen, et al.(P. Kristensen, et al., Phys. Rev. A 55), 978 (1997)., the electron affinity of He 1s2s\,^3S has been determined to high precision from both theory and experiment. The predicted affinity is 77.518(11) meV. Most of the uncertainties in this result come from the calculated nonrelativistic energy, --2.178\,077\,85(32) a.u. To further reduce this uncertainty, a large scale computation is carried out with a correlated wave function. Our 4258 term wave function gives an energy upper bound of --2.178\,078\,033 a.u. for He^- 1s2s2p\,^4P^o. The extrapolated energy is --2.178\,078\,044(11) a.u. Using this energy, the electron affinity becomes 77.5236(30) meV. The theoretical uncertainty is reduced by a factor of four. The predicted affinity agrees with the experimental result of 77.516(6) meV^2 .

[GP01.36] Operator expansion for relativistic multiconfiguration calculations

Relativistic multiconfiguration calculations( F.A. Parpia, C. Froese Fischer and I.P. Grant, C.P.C. \textbf94,) 249 (1996) may involve large numbers of N-electron basis states formed from a few reference states by single and double substitutions to virtual orbitals. We write a matrix element of the hamiltonian between such basis states as a sum of 2-electron matrix elements multiplied by angular coefficients. We have succeeded in separating these angular coefficients into two kinds of quantities: (1) analytic factors which are explicit expressions involving the quantum numbers (n,l,j) of the virtual orbitals, and (2) numerical factors, independent of the virtual orbitals, containing the complications of antisymmetrization and coupling schemes. This allows the size of a calculation to be increased without recomputing the angular coefficients, and without increasing the amount of stored angular data. We present the analytic results and an outline of the derivations, done with the help of diagrammatic methods.(A.P. Jucys and A.A. Bandzaitis, \textitThe Theory of Angular Momentum in Quantum Mechanics) (Mokslas, Vilnius, 1977) Some numerical examples are also given.

[GP01.37] Alloying Behavior of some FCC Transition Metals from Simulation

The many-body, long-range potentials developed by Sutton-Chen [A. P. Sutton, J. Chen, Phil. Mag. Lett. \textbf61, 139 (1990)] (SC) are tested in the atomistic simulations of binary f.c.c. metallic alloys. As an example the alloying behavior of Ag-Au and Cu-Ni are studied at 300K using the Molecular Dynamics (MD) method. The MD algorithms that we use are based on the extended Hamiltonian formalism and the ordinary experimental conditions are simulated using the constant-pressure, constant-temperature (NPT) MD method. The enthalpy of mixing and density values of the random Ag-Au and Ni-Cu binary alloys are obtained as a function of concentration after 20000 to 25000 steps of NPT MD simulations. Simulation results are compared with the statically calculated values of Rafii-Tabar and Sutton [H. Rafii-Tabar and A. P. Sutton, Phil. Mag. Lett. \textbf63, 217 (1991)] and experiment.

[GP01.38] Theoretical Energy Levels of Fr-Like Ions.

The Dirac-Fock (DF) method has little difficulty in reproducing the energy level ordering and spacing of alkali atoms, Li through Cs, with a moderate accuracy even with the simplest wave functions, i.e., single configuration (SC) DF wave functions. However, SCDF wave functions for Fr-like ions (Z> 87) cannot even reproduce the level ordering of the valence electrons: 7s, 7p, 6d, and 5f including their fine structures. The exact positions of the 6d and 5f levels of Fr (Z=87) are not known, though the 5f_5/2 and 5f_7/5 levels are expected to be high. The 5f levels come down along the isoelectronic sequence of Fr, and eventually the theoretical level ordering becomes hydrogenic at Pa^4+ (Z=91), i.e., 5f_5/2 becomes the ground level followed by 5f_7/2, 6d, 7s, and 7p in that order. However, experimental level ordering for Th^3+ (Z=90) is already hydrogenic.(J. Blaise and J.-F. Wyart, Energy Levels and Atomic Spectra of Actinides), Tables Internationales de Constantes, Paris (1992). Reproducing the experimental positions of the 5f_j levels for Fr-like ions seems to be an extremely difficult theoretical challenge because both relativity and electron correlation must be treated fully and equally. We will report on the progress of alternative theoretical approaches we are testing to challenge this seemingly simple, yet demanding task.

[GP01.39] Hyperfine Structure Coupling Constants for He-like Ions

High precision calculations of the hyperfine structure coupling constants for the 2S and 2P states of He-like ions up to nuclear charge Z = 10 will be presented. The calculations include electric quadrupole interactions, and estimates of the relativistic, quantum electrodynamic, and finite nuclear size corrections. Results have been obtained for all known isotopes for which nuclear moments are available. In other cases, the calculations can be used to deduce the nuclear moments from measured hyperfine splittings. A comparison with experimental hyperfine splittings shows good agreement over the entire range of nuclear charge 2 \le Z \le 10 within the accuracy of the data, although there is some indication of a discrepancy which grows in proportion to Z^4.

[GP01.40] Simulation of Atomic Clocks with Unitary Integration

Unitary Integration(B. A. Shadwick and W. F. Buell, Phys. Rev. Lett., 79), 5189 (1997). is a numerical method that preserves the structure of the Liouville-von Neumann equation by evolving the density matrix \rho via unitary transformations, thereby preserving the kinematic invariants c_j=tr\rho^j,\ j=1,\ldots,n to all orders in the time step. Unitary integrators have been shown to be of particular utility when the time scales of interest are much greater than the characteristic time scales of the interaction. Atomic clocks represent such a system since the atomic coherence undergoes many oscillations in the course of a Ramsey interrogation time. In addition, high-Q atomic clocks represent a system where dissipation is weak. Unitary integration combined with an operator splitting approach to non-unitary evolution is an ideal technique for modeling such systems. We present results of numerical simulation of an atomic clock based on Raman resonance in a \Lambda system.

The Aerospace Corporation The Institute for Advanced Physics

[GP01.41] Density-Matrix Descriptions of Electromagnetic Interactions in Quantized Electronic Systems

Density-matrix descriptions have been developed to investigate the influence of relaxation phenomena during resonant and non-resonant radiative transitions of quantized electronic systems, including atomic systems and quantum-confinement systems (e. g., semiconductor microstructures). Radiative and collisional relaxation phenomena have been treated using Liouville-space projection-operator techniques. Both time-independent (resolvent-operator) and time-dependent (equation-of-motion) formulations have been developed. The self-energy operators that occur in these formulations can provide the basis for a self-consistent determination of the non-equilibrium and coherent electronic-state kinetics together with the spectral-line shapes.

[GP01.42] Calculation of Regge Trajectories Using their Analytic Properties in Energy.

Regge trajectories, generated by a superposition of Yukawa potentials, are evaluated using a simple (avoiding any kind of regulator) and efficient method \footnote C. Lovelace and D. Masson, Nuovo Cimento, Vol. XXVI, 3 (1962). based on the high energy Taylor series expansion of the trajectories. Their analytic properties in energy have been investigated in depth using Padé Approximations to effect the analytic continuation. Our study shows that different Regge trajectories are analytic continuation of one another in different Rieman sheets. Regge pole representation of scattering problems embodies deep physical insight; it leads to a new physical interpretation of diffraction scattering ( J. N. L. Connor, J. Chem. Soc. \small FARADAY TRANS.) 86, 1627 (1990).. Recently, it has been applied successfully to electron scattering \footnote Z. Felfli et al., Phys. Rev. Lett. 81, 963 (1998).. Our results are compared with those of previous authors \footnote D. Sokolovsky, C. Tully and J. Crothers, J. Phys. A31 1 (1998)..

Supported by NSF and DoE, Div. of Chem. Sciences, OBES, OER.

[GP01.43] Representability of reduced density matrices for many-electron systems

The ground state variational problem for an N-electron system may be formulated as one of linear optimization over the convex set of N-representable two-body reduced density matrices (RDM's) (A.~J.~Coleman, Rev.\ Mod.\ Phys.\ 35) (1963) 668--689; Claude Garrod and Jerome K.~Percus, J.\ Math.\ Phys.\ 5 (1964) 1756--1776.. We have found a new family of representability conditions by considering the expression I(k) = Tr\,\Gamma'.\Gamma-k\,Tr\,\gamma'.\gamma+k(k+1)/2, where (\gamma,\Gamma) are the one-body and two-body RDM's of the N-body system, (\gamma',\Gamma') are RDM's of an N'-body test system, and k is an integer in the range 0\leq k<\min(N',N). The known P and Q conditions are associated with N'=2; among our new conditions is I(1)\geq0 for N'=3. However, a conjecture that always I(k)\geq0 fails at \min(N,N')=4. In related work (Shidong Jiang et al., this Centennial Meeting.) we are re-investigating the practical application of semidefinite programming to the calculation of ground state properties, and are studying numerically the strength of old and new representability conditions.

[GP01.44] On Magnetic Dipole Interactions

We formulate a Dirac Hamiltonian for an electron in the field of a charged magnetic dipole, which can be solved exactly in the central field approximation. While no scattering resonances are found, we do find and describe three categories of bound-state solutions for this Hamiltonian which may represent the electron/positron system or possible new electromagnetic composites. One category of solution is a state with very strong binding energy (greater than the electron rest mass) but with only a small amount of kinetic energy. This state corresponds to a classical orbit picture in which the electric and magnetic forces are opposed and nearly balance each other. No bound states are found if the central magnetic dipole is uncharged.

[GP01.45] Using a Single Cycle Propagator to do Floquet Theory

We present examples of the use of a single cycle propagator in two-level and multi-level systems undergoing a sinusoidal interaction. This is equivalent to doing Floquet theory except that all multiphoton orders are included automatically. Among other things, this method is useful for strong oscillating fields with envelopes that are slowly varying compared to the frequency. The details of treating multi-level systems are discussed and the results are compared with experimentally measured values of the multiphoton Rabi frequency in the potassium 21s-19f system.

[GP01.46] Imaging Strong-Field Atomic and Molecular Dynamics

Imaging photoions and photoelectrons subsequent to strong-field ionization (atoms) and dissociative-ionization (molecules) is proving to be a valuable tool in deciphering complicated ejection dynamics. Recently, we have exploited our ability to collect ions and electrons over 4\pi sr to study angular and energy correlation between simultaneously ejected ions and electrons in atomic and molecular systems. In this poster we will present our results of electron-proton angular correlation subsequent to multiphoton dissociative-ionization of H_2 and triple correlation between atomic ions resulting from the total breakup of linear and bent triatomic systems. In addition, we will update our progress in the direct detection of non-sequential double ionization in atoms using our imaging spectrometer.

[GP01.47] Agreement of quantum and semiclassical approaches for above threshold ionization (ATI) of atomic Hydrogen in Rydberg states

Transition rates for two-photon ionization of H when photoionization is possible (ATI) don't have resonances. Therefore two-photon ATI of H in Rydberg states is convenient to investigate agreement between perturbation and semiclassical theories. To calculate ATI of H in the dipole approximation Sturmian expansion of Coulomb Green's function (CGF) is widely used. That allows to calculate ionization rates in states with main quantum number n<10. We got a modified Sturmian expansion for CGF that consists of two parts. The first part is similar to the well known expression of CGF with Whitteker's functions except that radial variables must not be interchanged. The other part is an infinite sum. Using modified CGF two-photon ionization rates for H in nl states are calculated for l up to 36 and n in some cases even up to 120. Ionization rate as function of n and \lambda/n^2 is presented in form of 2D and 3D graphics. Ionization rate Q_nl/I values for n\geq30 (l=1,2...10) are very close to each other. Semiclassical expressions for Q_nl and Q_n got by Bersons were used to compare quantum and quasiclassical theory predictions. There are good agreement for Q_n/I when n>10. At n>20 and 0

[GP01.48] On the Generation of Circularly Polarized Multiple High-Order Harmonic Emission From Two-Color Crossed Laser Beams

We present a scheme for the production of circularly polarized multiple high-order harmonic generation (HHG)( Xiao-Min Tong and Shih-I Chu, Phys. Rev. A 58) (1998) 2656.. The proposed experimental setup involves the use of two-color laser fields, consisting of a circularly polarized fundamental laser field and a linearly polarized second-harmonic laser field, in crossed beam configuration. The feasibility of such a scheme is demonstrated by an ab initio\ quantal study of the HHG power spectrum of He atoms by means of the time-dependent density functional theory with optimized effective potential and self-interaction correction recently developed( Xiao-Min Tong and Shih-I Chu, Phys. Rev A 57) (1998) 452.. The theoretical study also provides new insights regarding the different mechanisms responsible for the production of HHG in different energy regimes as well as the mechanism for the generation of continuous background radiation.

[GP01.49] Wavelet Time-Frequency Analysis of the Mechanisms in Multiple High-Order Harmonic Generation in Intense Pulsed Laser Fields

The quasiclassical three-step approximation (tunneling, free electron propagation in the laser field, and recombination with atomic core to emit radiation) is a popular model for the multiple high-order harmonic generation (HHG) phenomena in the tunneling limit. However, there are a number of subtle aspects of HHG such as lower order harmonics, threshold harmonics, fine structure in plateau harmonic peaks, and blue shift etc., cannot be explained by the quasiclassical model. Using precision time-dependent wave function obtained by the generalized time-dependent pseudospectral method( Xiao-Min Tong and Shih-I Chu, Chem. Phys. 217) (1997) 119., we have performed detailed time-frequency profile analysis of individual harmonic in various energy regimes for atomic H in intense pulsed laser fields using continuous wavelet transform^2. New insights on the subtle details of HHG mechanisms are obtained and the range of validity of the quasiclassical model assessed(Xiao-Min Tong and Shih-I Chu, Phys. Rev. A (submitted).).

[GP01.50] Exterior Complex Scaling - Generalized Pseudospectral Method for Complex Quasienergy Resonances: Application to Multiphoton Detachment of H^- Near the One-Photon Detachment Threshold

We introduce a new exterior complex scaling (ECS) method with generalized pseudospectral (GPS) technique for the determination of atomic and molecular resonances(D. A. Telnov and S.I. Chu, Phys. Rev. A (submitted).). The ECS-GPS procedure is numerically highly accurate and computational more efficient than the corresponding basis set -variational methods. It also provides a simpler procedure than the uniform complex scaling method for the calculations of partial rates and electron angular distribution. The ECS-GPS method is applied to the study of multi-photon detachment and electron angular distribution of H^- near the one-photon detachment threshold^1. The results are in good agreement with recent experimental data( L. Prastegaard, T. Andersen, and P. Balling, Phys. Rev. Lett. (submitted).).

[GP01.51] Time-Dependent Density Functional Theory With Optimized Effective Potential and Self-Interaction Correction for Molecular Multiphoton Processes in Intense Pulsed Laser Fields\

We develop a new time-dependent density functional theory (TDDFT) with optimized effective potential (OEP) and self-interaction correction (SIC) for ab initio\ nonperturbative treatment of multi-electron molecular multiphoton dynamics in intense pulsed laser fields(X. Chu and S. I. Chu, Chem. Phys. Lett. (submitted).). The theory overcomes the shortcoming of traditional DFT/TDDFT and provides an accurate description of both short and long range potentials, yielding accurate eigenvalues for both individual orbital energies and the ionization potential. The time-dependent wave function can be accurately and efficiently propagated by means of the generalized pseudospectral time-dependent procedure(X. M. Tong and S.I. Chu, Chem. Phys. 217) (1997) 119. on non-uniform grid lattice. The theory and method will be illustrated by the case study of multiphoton ionization, high-order harmonic generation, and Coulomb explosion of H_2 and N_2 molecules^1.

[GP01.52] Dark state splitting in 4-level system

Four-level system under four strong fields with frequencies to combine into a cycle is analyzed for double-\Lambda scheme. A new simple algebraic criterion of coherent population trapping is suggested. The dark state is found to split, i.e., arises at two values of the detuning, as opposed to the three-level case. The splitting is shown to manifest itself as two sharp dips in the frequency dependence of the upper level population; repulsion between the nonabsorbing states is demonstrated when Rabi frequencies exceed relaxation rates. Similar dips are found in nonlinear susceptibility, which is responsible for the conversion efficiency of resonant four-wave mixing.

[GP01.53] Intensity Dependence of the Plateau Structure in Laser-Assisted, X-Ray--Atom Scattering Processes.

The intensity dependence of the recently discovered (D. B. Milo\vs)evi\'c and F. Ehlotzky, Phys. Rev. 58, 2319 (1998). plateau structure in laser-assisted x-ray--atom scattering is analyzed for stronger laser fields. Using the ``three-step'' model and the strong-field approximation we show a connection between this process and high-order harmonic generation. For x-ray--atom scattering in the presence of a static electric field for higher laser field intensities a new plateau appears which is 5 orders of magnitude higher than the recently discovered (D. B. Milo\vs)evi\'c and A. F. Starace, Phys. Rev. Lett. 81, 5097 (1998). high-energy plateau. The position, as well as the height, of these plateaus is explained using semiclassical arguments. Supported in part by NSF Grant No. PHY-9722110.

[GP01.54] Control of High-Harmonic Generation with Parallel Static Electric and Magnetic Fields.

We consider the possibility of control of high-harmonic generation in a linearly polarized laser field by adding static electric and magnetic fields which are parallel to the laser polarization. We show that the magnetic field can considerably increase the harmonic intensity. A chosen harmonic is emitted with maximum efficiency for such values of the B field for which the classical period of the electron's motion perpendicular to the magnetic field is equal to the return time of the laser-field ionized electron wave packet to the nucleus. While the static magnetic field has only a small effect on the position of the cutoff, the static electric field can introduce additional plateaus and cutoffs. A properly chosen combination of the static electric and magnetic fields can increase both the harmonic intensity and the harmonic order. Supported in part by NSF Grant No. PHY-9722110.

[GP01.55] Polarization and Static Electric-Field-Induced Effects on Harmonic Generation (HG)

The general structure of the atomic dipole moment vector and nonlinear susceptibilities are analyzed for an arbitrary geometrical arrangement of an elliptically polarized laser and a static electric field. For an n-th order harmonic, we present its intensity, ellipticity, polarization ellipse orientation, elliptical and circular dichroism effects, and phase relative to the pump laser. We find that polarization effects in HG with and without a static electric field are very different. Particular effects discussed include static-field-induced HG by circularly polarized lasers and dissipation-induced ellipticity and circular dichroism by linearly polarized lasers. Quantitative numerical predictions of these effects and their dependence on appropriate geometrical and dynamical parameters are presented.

[GP01.56] Changes in Floquet-state structure at avoided crossings: Delocalization and harmonic generation.

We examine the sinusoidally driven particle in a square potential well to show that avoided crossings in the quasienergy spectrum can alter the structure of Floquet states in this system (T. Timberlake and L. E. Reichl, quant-ph/9810014). Two types of avoided crossings are identified: one type leads only to temporary changes (as a function of driving field strength) in Floquet state structure while the second type can lead to permanent delocalization of the Floquet states. Radiation spectra from these latter states show a significant increase in high harmonic generation as the system passes through the avoided crossing. Both avoided crossings and high harmonic generation in the quantum system can be associated with the spread of chaos in the classical system (W. Chism, T. Timberlake, and L. E. Reichl, PRE \textbf58), 1713 (1998). The delocalization that occurs at the avoided crossings leads, at high field strengths, to Floquet states that fill the classically chaotic region. The cutoff in the high harmonic generation is then determined by the energy width of the chaotic region.

[GP01.57] Light-induced Atomic States and Diabatic Paths in Intense Laser Fields

The physical reality of light-induced states (LIS) in atoms has remained uncertain, ever since their discovery by Floquet theory. We have shown that their existence is confirmed by time-dependent wave packet theory, and should manifest itself experimentally(J.C.\ Wells, I.\ Simbotin, and M.\ Gavrila, Phys.\ Rev.\ Lett.\ 80), 3479 (1998). By applying a realistic pulse to the atomic system, and calculating the energy spectrum of the ionized electrons, we find signals at the energies predicted by Floquet theory for the LIS, sometimes with towering intensity. Choosing the initial states such as to connect to the LIS via diabatic Floquet paths substantially enhances the yield. The physical reality of LIS has far reaching consequences for strong-field dynamics. After materialization, the LIS behave like any other Floquet state, and, together with the Floquet states which continue the stationary states of the atom, determine the spectral properties of the atom in the field. The LIS are a reservoir of states participating as intermediate steps in EPI/ATI, HHG, several-color excitation, and stabilization dynamics, and offer paths of evolution of the atom to super-high intensities.

[GP01.58] Angular Distributions of Photoelectrons in Above-Threshold Ionization

A calculation of the angular distributions of photoelectrons produced in above-threshold ionization has been performed according to a recent theory(J. Gao, D.-S. Guo and Y.-S. Wu, to be published), which extends the scattering theory of Guo, Åberg and Crasemann by inclusion of spontaneous emission, at the beam intensities with a noninteger ponderomotive parameter. The calculation shows qualitative agreement with experimental results.

[GP01.59] Inclusion of Electron Dynamics in a 3D Global Gyrokinetic Particle Model

Recent experimental results have underlined the importance of the electron channel in understanding the tranport of particles and heat at the core of present day tokamaks. We have embarked on a program which aims at including electron dynamics in our three-dimensional global electrostatic gyrokinetic code used to model ion temperature gradient driven turbulence (ITGDT) but with adiabatic electrons. A drift kinetic, guiding center description of the electrons, including mirroring, has been deemed adequate and is being implemented using a delta-f framework which is also used for the gyrokinetic ions. A time-implicit treatment has been adopted to avoid the fast time scales, hence small time steps, associated with the motion of the electrons parallel to the magnetic field. In addition to exploring the properties of delta-f descriptions for more than one species of particles, applications of this massively parallel modeling tool, will range from ITGDT to current self-generation and sustainment.

[GP01.60] Effect of Magnetic Shear Reversal on the Parallel Velocity Shear Instability

The nonlinear behavior of the parallel velocity shear instability in a sheared magentic field is studied. It is found that when the magnetic shear as has the same sign as the second radial derivative of the parallel velocity profile, the instability is destabilized even further than if there were no magnetic shear. When the magnetic shear is reversed, the instability is considerably weaker. This effect is consistent with the observed reversed shear stabilization observed in tokamaks for the case of field-aligned flows. A physical mechanism is presented that explains this phenomenon, and it is shown that this effect may be a common feature of all instabilities with a mode structure both the parallel and perpendicular to the magnetic field.

[GP01.61] A Multi-Grid Algorithm for Nonlocal Collisional Electrostatic Drift-Wave Turbulence

We have developed a three-dimensional anisotropic multi-grid solver for simulating nonlocal collisional electrostatic drift-wave turbulence in the presence of magnetic shear. This solver has been used to obtain entire flux surface solutions of the nonlocal Hasegawa--Wakatani equations. In contrast with flux-tube models, which necessarily require approximation of the parallel boundary condition, the solution of a full tokamak flux surface in field-line coordinates allows the doubly periodic boundary condition to be expressed without approximation. The implicit treatment of the parallel-gradient terms permits the use of a relatively large time step. Considerable effort was made in the design of the implicit solver to ensure that the presence of anisotropy does not lead to a significant degradation in performance. The multi-grid algorithm has several advantages over a pseudospectral Poisson solver; most importantly, all nonlinear terms, including those in the Ohm's law, can be retained in a straightforward manner. Although in this work the multigrid method is illustrated using straightened tokamak geometry, the object-oriented construction of the code will facilitate the eventual inclusion of curvature terms and the complete nonlinear reduced Braginskii equations, including ion thermal dynamics.

[GP01.62] A Dynamical Model of "Avalanches"

The currently popular self-organized criticality paradigm rests on the concept of an avalanche. In a cellular automaton model, an avalanche is simply a coherent chain of topplings. In plasma dynamics, avalanche concept suggests the notion of an "event", where several adjacent modes collectively act to drive a burst of enhanced transport. "Transport events" or "avalanches" have been observed in numerical simulations, but the dynamics of avalanches remains obscure.

Here, we propose that the "avalanche" is a collective excitation in the gas of waves, - i.e. a radially extended, poloidally thin modulational wave or instability. Thus, an avalanche is, effectively, a streamer. We develop this proposal by examining the modulational stability of streamers in a gas of interchange - thermal Rossby modes. A streamer stability criterion and growth rate have been calculated. Streamers/avalanches are excited by both a turbulent Reynold's stress and by turbulence - enhanced pressure. The back-reaction of streamer events on the underlying turbulence is the subject of an ongoing study, as is the interplay between streamers and zonal flows.

[GP01.63] Self-Organizied Criticality and Force-Free States

Here, we examine force-free magnetic field states in a bath of noise. In terms of the transport SOC paradigm(D. E. Newman, et. al., Phys. Plasmas 3), 1858 (1996). the marginal profile is the force-free state, known to be marginal to tearing. The conservation law is that of magnetic helicity. Enforcing minimum energy determines the marginal profile. Deviations from marginality can be represented by an equation for the force-free parameter (ratio of parallel current to magnetic field), or an equation for helicity transport. These deviations can be generated by resistive dissipation, and the fluxes can be represented by alpha and beta effects, as well as the novel fluctuation generated hyper-resistivity (analogous to water running down an inclined plane.) In analogy with transport paradigms, SOC states can be sub-marginal, which for force-free marginality, results in a lowering of the minimum of the minimum energy state.

[GP01.64] Fundamental Transport Suppression Mechanisms arising from Reversed Magnetic Shear and Radial Electric Field Shear

A fundamental understanding of transport barriers in tokamaks is presented in terms of drift wave maps which are sympletic representations of the guiding center differential equations for the charged particle motions in tokamaks with fluctuations. Ensembles of test particles launched from the core of the tokamak are advanced forward in time to determine the effect of various rotational transforms profiles on the global particle confinement. The global confinement time is show to be enhance for particles that have a shearless winding number in their map. The winding number for electrons depends principally on the magnetic field rotational transform and shows enhanced confinement for Reversed Magnetic Shear Profiles (RS) plasmas. The winding number of the ions depends on both the magnetic-q profile and the rotation from the radial electric field. Thus, the confinement enhancement for ions can be strongly improved by deep wells in the radial electric field profile. Neoclassical theory is used to calculate self-consistient profiles of Er for the both monotonic and reversed magnetic shear profiles for particular TFTR discharges. The orbits of the full guiding center and those from from the sympletic maps are different as shown in detail. The ensembled averaged global confinement properties from the two approaches are thought to track one another. A third approach using reductions two low-order moments from stochastic differential equations that include the effect of the Coulomb collisional scattering of the charged particles is also compared with the drift wave map confinement predictions.

[GP01.65] Kirchhoff Thermal Radiation - The Cause Behind Anomalous Transport

The principal toroidal transport anomalies, namely, (i) enhanced particle and thermal diffusivity, (ii) magnetic-field dependence, (iii) temperature dependence, (iv) density dependence, (v) isotope-mass dependence, and (vi) power degradation in auxiliary heated plasmas, are all traced to momentum-exchange collisions induced via Kirchhoff thermal radiation(S. Puri, Phys. Plasmas \bf5), 2932 (1998). For the high-frequency Bernstein modes responsible for radiative collisionality, the product of frequency and plasma parameter greatly exceeds the two-particle collision frequency; the expansion procedure in terms of the plasma parameter used in the Balescu-Lenard type of equations is not applicable. Thus, Kirchhoff's law is the only presently available method for determining radiative collisionality. The simple yet rigorous approach allows important insights into the basic mechanisms responsible for toroidal transport and possesses definite predictive capability for reactor-scale plasma performance.

[GP01.66] The gyro-radius scaling of ion thermal transport from global numerical simulations of ITG Turbulence.

A three-dimensional fluid code is employed to study the scaling of ion thermal transport caused by Ion-Temperature-Gradient-Driven (ITG) turbulence in a tokamak, and in particular the dependence of the effective ion thermal conductivity \chi_i on the reduced gyroradius \rho_\displaystyle * \equiv \rho_s/a, where \rho_s is the ion sound Larmor radius and a the machine minor radius. The code includes toroidal effects and is capable of simulating the whole torus. It is found that both close to the ITG threshold and well above threshold, the thermal transport exhibits the gyro-Bohm scaling \chi_i / \chi_B \sim \rho_\displaystyle *, where \chi_B is the Bohm diffusivity, at least for plasmas with moderate poloidal flow. This result is confirmed by the analysis of some quantities that characterize the turbulent fluctuations (correlation lengths and time and the fluctuation level), which also exhibit gyro-Bohm scaling.

[GP01.67] Mean Field Transport Equations Including E x B Velocity

The stabilization of turbulence by E\times B velocity shear has been incorporated into models of tokamak transport in a number of forms. The radial electric field is determined by the perpendicular and diamagnetic velocities through the radial force balance for the ions. Thus, the E\times B velocity shear involves the second derivative of the ion pressure. This make the system of transport equations of third order in the pressure gradient. It has recently been pointed out that the solution one obtains can be stongly influenced by the choice of boundary condition for the second derivative of the pressure.(J.B. Taylor et al.), Phys.\ Plasmas 5 (1998) 3065. The choice of this boundary condition is undertermined by the physics. In this paper a systematic derivation of a set of mean field transport equations is presented. The turbulent fluxes are averaged over the instability time and length scales. The fluxes only involve first derivatives of the fields. An equation for the evolution of the E\times B velocity is derived. Physically motivated boundary conditions exist for all of the fields. The poloidal velocity is determined from radial force balance. The poloidal velocity can strongly deviate from its standard neoclassical value due to the perpendicular turbulent viscosity.

[GP01.68] Parallel Velocity Shear Driven Modes in Discharges with Reverse Magnetic Shear

The linear and quasilinear behaviour of the short-wavelength drift-like perturbation with a parallel velocity shear is studied in a sheared slab geometry. Full analytic studies show that when the magnetic shear has the same sign as the second derivative of the parallel velocity with respect to the radial coordinate, the linear mode may become unstable and turbulent momentum transport increases. On the other hand, when the magnetic shear has opposite sign as the second derivative of the parallel velocity, the linear mode is completely stabilised and turbulent momentum transport reduces. This result therefore shows that it is the relative sign of the second radial derivative of the equilibrium parallel flow with respect to the magnetic shear which is the key factor for the enhance reverse shear transition.

[GP01.69] Local Scalings and Nonlocal Effects in Toroidal ITG Turbulence

We report new results on toroidal ITG turbulence from nonlinear gyrokinetic simulations. (A) For some ion temperature gradient scans, the local ion thermal flux \Gamma is found to be very accurately described by a form \Gamma \propto \partial_r T - \partial_r T|_eff, where \partial_r T|_eff is an effective critical temperature gradient that is larger than the linear critical temperature gradient. The excellence and simplicity of the fit, including the ability to obtain \partial_r T|_eff by extrapolation from values of \Gamma with \partial_r T > \partial_r T|_eff, suggest a considerable simplification of the underlying physics. The robustness of this dependence to various physical effects and parameter variations will be explored.

(B) A new analysis method, based on scatter plots of radially local time-window-averaged thermal flux vs.\ gradient, has been applied to explore whether the transport in global gyrokinetic simulations is local. For profile variation scales characteristic of DIII-D, the transport is found to be nonlocal; there are regions of low and high temperature gradient where the transport is respectively significantly larger and smaller than the local prediction. A sequence of larger simulation runs is underway to investigate when a transition to local behavior occurs.

[GP01.70] Negative-energy perturbations and reversed-magnetic-shear transport barriers in tokamaks

The impact of reversed magnetic shear (s<0) along with a radial electric field E_r on negative-energy perturbations (NEP's) is investigated for the case of cylindrical tokamak-like equilibria. NEP's can imply instabilities leading to anomalous transport [G. N. Throumoulopoulos and D. Pfirsch, Phys. Rev. E 56, 5979 (1997) and Refs. therein]. For equilibria with E_r=0 and \eta_\nu<4/3 (\eta_\nu\equiv \partial\ln T_\nu /\partial\ln N_\nu, and \nu denotes the particle species) s<0 results in a reduction of the fraction of particles associated with NEP's (active particles) in comparison with that for equilibria with s>0, by making the pressure profile steeper. The reduction is stronger the closer the minimum of the safety factor (q_\min) to the plasma center and the lower the negative value of s. For equilibria with E_r < 0 a reduction of the fractions of active ions for \eta_i<4/3 and of active electrons for \eta_e>4/3 is caused by E_r irrespective of the sign and the value of s and of the position of q_\min. The present results indicate that the effect of s<0 on NEP's is not additive to that of E_r. Also, it is shown that the experimentally evidenced facts that (a) s<0 is associated with a steepness of the pressure profile and (b) the position of q_\min is displaced towards the plasma edge as the toroidal current is increased are consistent with equilibrium considerations.

[GP01.71] Electromagnetic, Nonlinear Gyrokinetic Simulations

A widely used, comprehensive linear gyrokinetic code(Kotschenreuther, M., et al.,) Comp.~Phys.~Comm., 88, 128 (1995). has been generalized to be both massively parallel and nonlinear. The simulation domain is a flux tube set in general toroidal geometry. This code evolves distribution functions for electrons and an arbitrary number of ion species in time on a grid in three spatial dimensions, energy, pitch angle, and the sign of the parallel velocity. Trapped particle dynamics are fully included, and collisional effects are treated with a Lorentz collision operator. In each direction, non-uniform coordinate grids are chosen to maximize resolution where needed. A simulation domain of 48*96*96*10*60*2 uses 500 million grid points for each species. Thus, good parallel performance is required. To attain this goal without compromising portability, we have completely rewritten the original code using object oriented methods; the resulting code runs correctly on multiple MPP platforms. Available computational and physics results will be presented.

[GP01.72] Effective Field for Turbulent Transport in Shaped Tokamak Plasmas

The nonlinear ballooning mode code(R.E. Waltz et al.), Phys.\ Plasmas 1 (1994) 2229; ibid.\ 5 (1998) 1784.\ for ITG turbulence now has a generalization(R.L Miller et al.), Phys.\ Plasmas 2 (1998) 973.\ of the circular \hat s-\alpha local MHD equilibrium model to finite aspect ratio (A), elongation (\kappa), and triangularity (\delta). This allows us to make systematic studies of shaped flux surfaces with the same minor midplane radius lable (r), plasma gradients, q, \hat s, and \alpha, while varying A, \kappa, and \delta. We show that the (linear, nonlinear, sheared) E\times B terms in the equation of motion are unchanged from a circle at radius r with an effective field B_unit=B_0\rho d\rho/rdr where \chi=\rho^2/2 is the toroidal flux, and r is the flux surface label. This leads to a ``natural gyroBohm diffusivity'' \chi^natural which at moderate q=2--3 is weakly dependent on shape (\kappa) at fixed B_unit. However since B_unit/B_0\approx\kappa (or larger), the label independent \chi^ITER=(B_0/B_unit)^2\chi^natural/ \langle(\nabla r)^2\rangle at fixed B_0 scales as 1/\kappa^1.6 (weaker scaling at high-q and stronger at low-q). Linear stability is not a good indicator of scaling with \kappa. The generalized E\times B shear rate to be compared to the maximum linear growth rate^2 is a flux surface quantity (r/q)d/dr(cq/rB_unitd\phi_0/dr) =(r/q)d(cE_x0/B_\theta R)/dr.

[GP01.73] Turbulence Simulation Using A Gyrokinetic Ion-Fluid Electron Hybrid Model

We describe the formulation of a hybrid model with fully gyrokinetic ions and zero-inertia fluid model for electrons. The electron fluid equations are derived from moments of the drift kinetic equation, taking m_e\rightarrow0, but with T_\parallel e finite, thereby avoiding all accuracy or stability constraints on k_\parallel v_te \Delta t, as well as particle noise associated with electron free streaming. This approach is a natural extension of the electrostatic gyrokinetic simulations to include effects of electron ExB flow, electron pressure gradient effects (e.g. ømega_*e), and most importantly the electron parallel current, which in turn is used to include electromagnetic perturbations perpendicular to the equilibrium B-field (\delta B_\perp). A nice property of this model is that it includes the shear Alfvén wave physics while eliminates high frequency waves associated with the electron inertia, and is therefore suitable for studying the \beta! d! ependence of ITG driven microins tabilities (including the recently discussed Alfvén ITG(Zonca et. al.), Bull. Am. Phy. Soc. 43(8), 1921(1998)). A predictor-corrector scheme for the hybrid model has been developed for the simulation of a flux-tube. Details of this integration scheme will be presented, with an emphasis on benchmarking the shearless slab result aginst the local dispersion relation. Preliminary results for a toroidal flux-tube will also be presented and discussed.

[GP01.74] 3D Simulations of Tokamak Edge Turbulence in General Geometry

In past work(B. N. Rogers, J. F. Drake, A. Zeiler, Phys. Rev. Lett. 81), 4396 (1998) we described a model for the LH transition and density limit in tokamaks based on 3D flux tube simulations of edge turbulence. The simulations were based on the the Braginskii equations and assumed a simple shifted circle magnetic geometry. At a qualitative level, the predictions of the model show encouraging agreement with experimental data in CMod, DIIID, and ASDEX-U. Quantitatively, however, substantial uncertainty arises in the comparison of the model to experiments due to the absence of realistic magnetic shaping effects in the simulations. We report on here our progress toward including such shaping effects into our 3D simulations of edge turbulence and the impact these effects have on the simulated anomalous transport.

[GP01.75] Thermal Transport Coefficient for L-Mode Discharges

Starting from an analysis of the transport properties of the plasmas produced by the Alcator C-Mod machine, a novel form of a thermal transport coefficient(B. Coppi and W. Daughton, in 24^th) EPS Conference on Controlled Fusion and Plasma Physics, (1997) which reproduces both ohmic and auxiliary heated L-mode discharges has been identified. This thermal transport coefficient involves the difference of two terms, one representing the normal outward diffusion of thermal energy and the oth er corresponding to a process reducing the outward flux. The coefficient includes the constraint of profile consistency and is inspired by the properties of the toroidal ion and electron temperature gradient modes. In a series of transport simulations for plasmas produced by the Alcator C-Mod machine, the thermal transport coefficient is shown to reproduce the observed electron temperature profile, stored energy and loop voltage. The relevant scaling for the energy confinement time is also composed of t wo terms. The L-mode database assembled for the ITER project is used to compare DIII-D, JET, JT60, PDX, TFTR, FTU, and Alcator C-Mod with this analysis. With the exception of PDX, the comparison is substantially better than standard L-mode pow er law scalings.

[GP01.76] 3D Global Gyrokinetic Particle Simulation Study of Turbulence Suppression in Neon Impurity-Seeded Tokamak Plasmas

Recent experiments have shown that improved confinement regimes of tokamak plasmas can be obtained through a controlled introduction of a radiating impurity such as Neon or Argon. There is also evidence that turbulent fluctuations are being suppressed as the impurities are being distributed. We have been investigating the physical processes involved in turbulence suppression under these conditions using experimentally determined temperature, density, and magnetic field profiles taken before and after impurity injection in the TEXTOR-94 tokamak plasma. We use a nonlinear 3D global toroidal gyrokinetic particle simulation model which contains multiple ion species (R.D. Sydora, V.K. Decyk and J.M. Dawson, Plasma Phys. Contol. Fusion, 38,p.281,(1996). Self-generated turbulent zonal flows from flux surface-averaged potentials as well as equilibrium sheared ExB flows are included in the model. Preliminary results indicate that suppression of toroidal ion temperature gradient instabilities occurs as a result of density peaking from reduced particle transport and direct stabilization of ITG modes via dilution and impurity gradient effects. Scaling studies with various parameters such as impurity concentration and gradient will be presented.

[GP01.77] Split-Weight \delta f Gyrokinetic Particle Simulation Scheme for Finite-\beta Plasmas

A split-weight \delta f gyrokinetic particle simulation scheme for finite-\beta plasmas have been developed. This is an extension of the electrostatic version of the split-weight scheme^1. In this scheme, the standard \delta f response is splitted into an adiabatic part and an nonadiabatic part, with the latter followed dynamically for each particle. Since the phase velocities for the waves of interest, such as shear-Alfven waves, are usually much smaller than the electron thermal speed for \beta \gg m_e/m_i, the nonadiabatic responses for most of the electrons are nearly zero and do not contribute to the velocity moments. Thus, the parallell Courant condition of k_\parallel v_\parallel \Delta t \ll 1 for the fast particles can be circumvented resulting in considerable increase in time steps for the code as well as the reduction of noise from the fast moving particles. The use of the split-weight scheme based on the generalized Ohm's law^2 as well as the p_\parallel formalism^3 for studying shear-Alfven waves and their coupling with drift waves and ion temperature gradient modes will be presented.

^1 I. Manuilskiy. W. W. Lee, and H. Mynick, Bull. Am. Phys. Soc. 43, 1723 (1998). ^2 J. Reynders, Ph. D. thesis, Princeton University, 1992. ^3 T. S. Hahm, W. W. Lee, and A. Brizard, Phys. Fluids 31, 1940 (1988).

[GP01.78] Gyrokinetic Solver on Linux Beowulf

Progress on a parallel, full-radius, electromagnetic, gyrokinetic, Eulerian (fluid-like) code is detailed. In particular, we emphasize the inclusion of passing electron dynamics required for electromagnetic perturbations. The electron parallel motion is treated using implicit numerical methods, so that the requisite short time-step of any explicit method can be avoided. We hope to elucidate the role of profile effects in plasma transport using a formalism free of uncertainties related to fluid closures, particle noise, and the restriction to electrostatic perturbations.

The development platform is a 16-node parallel distributed memory Linux Beowulf cluster supporting MPI interprocessor communication. Such a developent environment is ideal for the production of comparitively stable, well-documented, bug-free, and portable code. We expect this code to migrate easily to future TFLOP machines which provide the vast computational resources necessary for production runs.

[GP01.79] A Framework for Gyrokinetic Particle Simulation of Electromagnetic ITG Turbulence

There has been a recent growth in interest in electromagnetic effects on tokamak plasma turbulence and anomalous density and energy transport. Earlier studies of linear ion-temperature-gradient (ITG) driven instabilities have indicated that the electrostatic ITG mode is strongly suppressed by finite plasma beta. More recently, it has been theorized that Alfvén modes in the continuum gap may be discretized by finite-Larmor-radius (FLR) and finite-orbit-width (FOW) effects and driven unstable at a plasma beta well below the ideal MHD critical value. Furthermore, experimental results indicate disparate behaviors in the ion and electron thermal transport channels in response to certain changes in plasma conditions, which may be an indication that electromagnetic perturbations are playing a more important role in electron transport than previously thought. Thus, the need for intensive study and simulation of electron dynamics and electromagnetic turbulence has never been greater. In order to address these issues, we propose a general framework for gyrokinetic particle simulation of electromagnetic perturbations. This framework will be structured in a way that will allow various models for different plasma species, geometries, perturbative quantities and plasma diagnostics to be easily interchanged in a ``plug-and-play'' environment. In this way, we can use the same code base to simulate Alfvénic ITG modes, energetic particle modes, and trapped-particle effects, all with a choice of models for the electron dynamics. We describe here the workings of our framework approach and how it allows us to leverage our software development and attack several interesting physics problems at once.

[GP01.80] Coupling Transport and Turbulence in Edge-Plasma Simulations

The collisional edge region of a tokamak is often described by fluid equations for plasma density, parallel velocity, electron and ion temperatures, and electrostatic potential. Transport codes such as UEDGE use empirical diffusion coefficients for transport across the magnetic field, B, to evolve these variables in 2-D over long space and time scales to obtain equilibrium profiles. Turbulence codes such as BOUT typically use fixed profiles to calculate the 3-D turbulence on shorter space and faster time scales, yielding physics-based cross-field fluxes or diffusion coefficients. We present initial results of an iterative coupling between UEDGE and BOUT over the pedestal gradient edge-region and the scrape-off layer outside the magnetic separatrix giving a self-consistent simulation. Of particular importance is the generation of a strong radial electric field with rapid radial variation which produces a sheared E \times B flow that helps suppress turbulence, thereby creating an H-mode transport barrier in the edge-region. The dynamic evolution of plasma profiles and turbulence is necessary to identify the trigger mechanism for L-H mode confinement transitions. An assessment is given of the computational resources required to perform these coupled simulations on a routine basis.

[GP01.81] Progress in Nonlinear Gyrokinetic Simulation

Progress in nonlinear gyrokinetic simulation of turbulent transport in tokamaks is reported. We are porting our general noncircular-cross-section equilibrium capability(A.M.\ Dimits, Bull.\ APS 41), 1413 (1996). to our parallel (T3E) flux-tube gyrokinetic code. Initial results will be shown using both reconstructed DIII-D equilibria and equilibria from MHD equilibrium solvers, focusing on benchmarks and convergence tests made possible by the the implementation of this physics on larger computers. A new bounce-averaged drift-kinetic \delta f electron algorithm has been formulated and is being implemented in our gyrokinetic code. Linear benchmarks and initial studies addressing the effect of nonadiabatic electrons on ITG turbulence and transport will be presented. Results of continuing studies of the convergence of our gyrokinetic simulations with respect to particle number, grid size, and system size, as well as dependence on initial conditions will also be presented.

[GP01.82] A nonlinear correction to Landau-fluid closures suitable for gyrofluid turbulence simulations

An simple to use method for calculating the nonlinear correction to a given gyro-Landau-fluid closure term is presented. In order to calculate the nonlinear corrections, it is assumed the a reasonable linear closure term exists. This seems to be the case for existing gyrofluid equations which are fairly accurate linearly. In addition, perturbation theory is used, requiring the fluctuations to be small compared to the equilibrium values which is generally the case for drift-wave type tokamak turbulence. This approach introduces one more quantity to time evolve, but makes no reference to ømega or k_\perp, and is therefore well-suited for current pseudo-spectral simulations.

[GP01.83] Field-line Coordinates for Global Gyrokinetic Simulations

The field-line following magnetic coordinates has been implemented in the global gyrokinetic toroidal code (GTC). This enables us to take advantage of long parallel wavelength of microinstabilities believed to be responsible for transport in magnetized fusion plasmas. As a result, computational cost of a global simulation is dramatically reduced, and routine large scale simulations for the study of key issues in turbulent transport become possible. Our GTC code simulations have demonstrated decorrelation of nonlinearly saturated turbulence, and reduction of associated transport by self-generated zonal flows^1. Further studies show that ion-ion collisions can regulate transport via zonal flow damping. Close to marginal stability, turbulent damping of zonal flows is weak, and the saturation of the flows and thus the turbulent transport can depend on collisionality. Since effects of collisions have been neglected in most turbulent transport studies of high temperature plasmas, our results provide new insight into the transport scaling. Comparisons of simulations with analytic calculations^2 of the collisional flow damping will also be presented. \vspace0.1in

^1 Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. B. White, \hspace*0.1inScience 281, 1835(1998). ^2 F. L. Hinton and M. N. Rosenbluth, Proc. of the 25th Euro. Conf. \hspace*0.1inon Contr. Fusion and Plasma Phys., Praha, Czech Republic (1998).

[GP01.84] Effects of Temperature Ripples and Self Consistent Equilibrium E_r Shear in a Gyrokinetic Flux-Tube Simulation

Gyrokinetic simulations of ion-temperature-gradient-driven turbulence have shown the equilibrium E_r shear suppression of core ion heat transport. In addition, it has been shown that self-generated E_r shear is an important stabilizing effect, especially in flux-tube simulations. The present simulation includes all effects of pressure profile variation, including the equilibrium E_r shear from radial force balance, as well as the usual self-generated E_r shear. The self-generated purely radial electrostatic porential has been observed to be 180^o out of phase with the flux-surface-averaged perturbed perpendicular temperature. This correlation explains the different shapes of the purely radial modes found in various global and flux-tube simulations. Based on these observations, a novel method to reduce the ion heat transport is proposed. By introducing a temperature ripple as small as 2%, on a spatial scale of 30\rho_i, simulations have shown 60% reduction in the heat flux. However, these preliminary results did not include equilibrium E_r effects. It is possible that for some parameter values, these effects will cancel one another. We will present results that self-consistently include equilibrium E_r shear, as well as, a more detailed study of the parameters involved in the ripple transport suppression mechanism.

[GP01.85] A Theory of Edge Convection

Recently, a set of nonlinear model equations\footnote D.A. D'Ippolito, J.R. Myra, V. Bhatnagar, J. Jacquinot, Bull. Am. Phys. Soc. 43, 1755 (1998). was derived describing the interaction of driven convection with the tokamak edge plasma electric field and electron temperature T_e. For collisional plasmas described by the Braginkii equations, it was shown that strong convection could produce significant cooling and a reduction in the E \times B shear. The convection can be driven by a poloidal modulation of either the edge potential \phi (e.g. by ICRF heating) or the edge T_e (e.g. by gas puffing). Here, we extend the theory by solving the model equations numerically to obtain the scaling of the penetration of the convection. This work is motivated by experimental results on JET showing that 1) H-mode properties such as the ratio of \tau_E/\tau_p, the temperature pedestal height, and the ELM amplitude and repetition rate can be significantly different for ICRF H-modes under certain conditions (e.g. for low k_\parallel antenna phasing) than for NBI H-modes; and 2) there is an interesting parallel between the effects of ICRF and gas puffing on the H-mode. The relevance of this theory to JET and C-MOD experiments will be discussed.

[GP01.86] Resistive X-point modes in boundary plasmas

In recent work(X.Q. Xu et al., presented at the 17th IAEA Fusion Energy Conf., Yokohama, Japan, October 1998, paper IAEA-CN-69/THP2/03.) we have identified the curvature-driven resistive X-point mode as the dominant instability of a characteristic L-phase discharge in DIII-D. This mode, expected to be a generic L-mode edge/SOL instability, is electromagnetic near the outboard midplane, but transitions to an electrostatic mode near the X-point due to the combined effects of resistivity and X-point magnetic shear. Motivated by observations of elevated electron temperature near the X-point,(M.J. Schaffer et al., Bull. APS 43, 1889 (1998), paper R8P5.) we investigate heating and parallel energy flow induced by the resistive X-point mode. We speculate that energy in the unstable waves flows to and dissipates in the X-point region, heating the electrons. The mode is also expected to dominate perpendicular wave-induced transport. Modifications of the usual mixing length estimates to take into account the X-point geometry are shown to be required.

[GP01.87] Analysis of Anomalous Growth in Core Electrostatic Turbulence

Recent observations of large electron thermal transport in the flat temperature profile region of enhanced reverse shear (ERS) discharges suggests that nonlinear instability may play a role. Simulations of a two-field fluid collisionless trapped electron mode (CTEM) model show anomalous energy inputs and outputs at saturation which are localized in wavenumber but are not predicted by linear theory alone. This includes a mechanism for nonlinear anomalous energy growth. Prior results suggest that this is due to nonlinear excitation of a damped branch of the linear solution which is nonorthogonal to the growing branch, producing a frequency-dependent contribution to energy evolution. Through a variety of analytic techniques, including parametric excitation of the damped branch, iterative inversion of the nonlinear electron response, and analysis of nonorthogonal energy components, we will attempt to develop a deeper understanding of this effect and to predict and quantify it. We will also assess its role in an ion mixing mode (IMM) turbulence model, a variation of ion temperature gradient (ITG) turbulence which takes into account a nonadiabatic electron response.

[GP01.88] Impurity radiation and bursty plasma transport model

Impurity radiation (IR) plays an important role in the physics of edge plasmas. In "laminar" diffusive approach cross field plasma transport was shown to be one of the key element determining IR loss [1].However, there are indications that plasma transport may be far from "laminar" diffusion and is characterized by large bursts. We study nonlinear plasma transport model dT/dt=dDdT/dx/dx+S-R(T), where x is the spatial coordinate, T(x,t) is the plasma temperature , S and R(T) describe the heat source and IR sink, D=|dT(t-tau)/dx|**alfa is the plasma heat diffusivity, alfa is an adjustable parameter and tau a small time scale which can be interpreted as inverse growth rate of the plasma instability which result in nonlinear plasma heat diffusivity D. Tau though being very small causes the fine structures in our transport model to be unstable. As a result, transport becomes bursty and resembles SOC features. We report on the effects of our bursty transport model on IR loss and compare it with "laminar" transport models. [1] S. I. Krasheninnikov, Phys. Plasmas 4 (1997) 3741.

[GP01.89] 2-D Modeling of Ionization-Recombination Instability in the Edge Plasma*

Recent experimental findings in Alcator C-Mod tokamak [1] reveal that plasma strongly recombines in the MARFE region. Analysis of 0-D [2] and 1-D [3] models describing particle and energy balances shows that MARFE could be a non-linear stage of an ionization-recombination instability of hydrogen plasmas similar to that of a detachment front [4]. Based on a linear analysis of the instability for a slab geometry some 2-D model was built, allowing us to investigate numerically conditions for such an instability to appear. Here we report the results and compare our findings with the results of 0-D, 1-D models and experimental data. [1] B. Lipschultz et al., PRL (1998). [2] S. I. Krasheninnikov, et al., EPS-98. [3] A. N. Simakov, et.al., APS-98. [4] S. I. Krasheninnikov, et al., PSI-98.

[GP01.90] Kinetic Simulation of Coupled Plasmas and Neutral particles in the Scrape-off layer (SOL) of TdeV and in linear plasmas experiments.

In interesting detached regimes of TdeV, when the plasma detaches from the limiters, Coulomb Kudsen number increases with the local plasma gradients in an inhomogeneous magnetic field. Neutrals, which are being produced due to plasma recombination at the plasma-divertor interface, are also in a mixed collisional regimes. Thus, simultaneous kinetic treatments of plasma and neutral particles with self-consistent calculation of boundary conditions at the material walls are required. In linear machines, mirror effect due to inhomogeneous magnetic field and neutrals effects are very important. We present results for a kinetic simulation of plasmas and neutrals for actual conditions in TdeV and in a linear machine, where the effects of gradients and inhomogeneous magnetic field are taken into account.

[GP01.91] National Transport Code Collaboration (NTCC) Overview

NTCC is a multi-institutional collaboration whose goal is to change the way fusion modeling codes are constructed and used. The project includes extracting physics modules from existing codes and developing new modules. A review process has been developed to ensure that these modules satisfy well-defined standards. The accepted modules are placed in a Web-based community-owned NTCC module library. Modern computing techniques are used to construct a flexible framework, utilizing library modules, for the generation of easily maintained, customized, user-friendly transport codes that can be used to study new physics. This approach facilitates code use by non-experts and the examination of new transport models. Desktop access is provided through a browser to experimental data and to a physics server that can be located at remote sites. Data accessors enable examination of data in either U-file or MDS+ format. With the demonstration code that has been produced, the Multi-Mode, GLF23, IFS/PPPL, and OHE transport models can be compared and tested against experimental data.

[GP01.92] National Transport Code Collaboration Module Library

A library of computer code modules has been developed for the National Transport Code Collaboration (NTCC). Each module is an isolated, self-contained piece of software that is designed to carry out a specific function, such as the computation of the transport fluxes from a given model. After each module is submitted, it is evaluated by the Module Library Committee according to a list of standards. These standards require, for example, that each module is thoroughly documented and is provided with a stand-alone driver and test cases that compile and run correctly on different computer platforms. The resulting modules are intended to be easily inserted into transport codes and are available for anyone to use. Modules, standards, and additional information can be found on the Web page http://w3.pppl.gov/NTCC.

[GP01.93] Structure of the Demonstration Code for the National Transport Code Collaboration

The key concepts in the NTCC transport code are the use of plugable tokamak physics and numerical solution modules, steerable computations, remote invocation across the internet, interactive visualization of results, and automated retrieval of data using network transfers from remote MDSPlus data servers and Ufiles. The demonstration code features a physics server that is activated remotely within a standard web browser through application of CORBA technology. A Java-based gui client was developed that permits selection and interaction with various runtime control parameters and confiment models (GLF23, IFS\slash PPL, Multi-Mode, and OHE) and allows interactive graphical display of the resuslts as they are generated.

[GP01.94] Neutral Atom Transport Benchmark Studies

A validation study is being performed for the Transmission/Escape Probability (TEP) neutral atom transport method (W. M. Stacey, J. Mandrekas, Nucl. Fusion) 34 (1994) 1385., (W. M. Stacey, Phys. Plasmas) 4 (1997) 179.. The analytic formulation of the basic transport elements--the first-flight transmission and escape probabilities for a region--are being tested by comparison with exact results for slab geometry and by comparison with Monte Carlo for a range of geometries and region dimensions, and a new rational approximation is being developed for the escape probability. The accuracy of using of an average mean-free-path (mfp) to characterize a non-uniform region, which is done in the calculation of cumulative transmission and escape probabilities, is being tested. The isotropic incident flux assumption used in calculating transmission probabilities has been tested for multiregion transmission problems for regions of varying mfp, and an improved algorithm has been developed. Use of the local ion temperature to compute neutral mfps has been tested for non-uniform multiregion problems, and an iterative improvement is being developed. A multigroup formulation has been developed and will be implemented and tested. Accurate calculations of detailed scrape-off layer/divertor models of DIII-D, C-MOD and ITER require less than 1 min. of CRAY C90 time.

[GP01.95] Status of Physics Server for the National Transport Code Collaboration (NTCC) Demonstration Project

The NTCC demostration project utilizes modern software methodologies to develop a transport code that is easy to access, use, modify and maintain. We report on the structure and status of the physics application, presently a code which advances electron and ion pressure equations with density, flow, source and geometry profiles read in from a database. Modules for transport coefficients (typically Fortran) are wrapped and treated as class instances in an object-oriented heirarchy. Transport models available include IFS-PPPL, GLF23, and Multi-Mode. New modules, (e.g., neoclassical tranport, MHD equilbrium) will be added as they are made available through the NTCC Physics Module Library. We report on: the status of module installation; inter-model, inter-code, and data comparisons; tests of convergence of the models with various iteration schemes, physics complications (e.g., shear flow) and spatial representations; sensitivity to boundary conditions; and plans to upgrade to a fully predictive transport code.

[GP01.96] A Possible Confinement Time Barrier For Magnetic Fusion

One perplexing feature of the magnetic fusion program is the recent slow advance of the approach to "break even". One possibility is that there is a hidden physical limitation rather than the presently assumed engineering limitation. A past example of such a physical limitation is the scattering lifetime of the charged particles in the magnetic mirror machine being comparable to the break-even lifetime of Lawson's Criterion. An analogous limitation in present magnetic fusion devices may be simply black-body radiation. Any object that strongly absorbs radiation in a given frequency range must re-emit radiation as a black-body in the same frequency range. Let us make the simple assumption that a magnetically confined fusion plasma emits black body radiation over the frequency range in which intense RF heating has been demonstrated. The upper frequency limit may be set at the second harmonic of the electron cyclotron frequency(For example, see paper j5i2 by O. Motojima on p 1776, Bull. Am. Phys. Soc. Vol. 43, 8 (1998).). The lower frequency limit is set as zero. Assume an ideal fusion plasma of 10 exp 14 ions per cubic cm, an ion and electron temperature of 10 exp 8 degrees Kelvin, a magnetic field of 10 Tesla, and a volume of one cubic meter (Physicist's model.). Assume that this cube of plasma is emitting black body radiation from all six of its faces. Under these assumptions, the radiation lifetime for energy confinement is 11 seconds. This is rather close to the Lawson lifetime for break-even of one second. If emission occurs at higher harmonics, the situation is considerably worse.

[GP01.97] Advanced Tokamak Research at the DIII--D National Fusion Facility

The tokamak magnetic fusion concept has an enormous range of freedom to optimize its properties and potential as a fusion power system. Early tokamaks formed plasmas whose properties were largely derived from inductive pulse formation, with centrally peaked current profiles and low self-driven current fractions. In contrast, the AT concept utilizes: (1) non-monotomic current profiles, (2) electric and magnetic field shear to reduce plasma turbulence and subsequently energy transport; (3) plasma pressure and current profile control to optimize plasma pressure for high reactivity; (4) self-driven bootstrap currents to enable efficient steady-state operation; and (5) divertor design to provide power dispersal and particle control to sustain plasma purity with intense power and particle exhaust. This paper reports \hboxDIII--D experimental progress in these individual research areas as well as their optimized integration and theoretical modeling toward demonstrating the advanced tokamak concept.

[GP01.98] A Theoretical and Experimental Investigation into Energy Transport in High Temperature Tokamak Plasmas

In the design of next step fusion devices the energy confinement time (\tau_E) has been identified as a critical parameter. Efforts to predict \tau_E in future machines has centered around three different techniques: statistical analysis of global energy confinement data, a dimensionless physics parameter similarity method similar to aircraft wind tunnel experiments, and modeling of cross-field turbulence driven energy transport. Early statistical work proved quite accurate in predicting future machine performance. Valuable insight into energy transport has been obtained in wind-tunnel like experiments involving experimental data from the international fusion community. Recent advances in theoretical modeling have increased our understanding of the underlying physics that determines global confinement. New experiments using a modulated heat source and varying the ratio of electron to ion temperature have allowed detailed comparisons to theories. A discussion of the three techniques will be presented.

[GP01.99] A Comparison of Fueling with Deuterium Pellet Injection from Different Locations on the DIII-D Tokamak

Deuterium pellet injection has been used in experiments on the DIII-D tokamak to investigate several aspects of plasma confinement and density control. The measured fueling efficiency and deposition profiles from pellets injected from the outer midplane show a large discrepancy with pellet ablation theory, while the penetration depth compares favorably with theory. An apparent outward displacement of the deposited pellet mass is observed and is hypothesized to occur from \nablaB induced drift effects. Vertical injection of pellets 20 cm inside the magnetic axis has been employed on DIII-D to investigate these effects. The results show pellet mass deposition inside the expected deposition radius, suggesting that a drift of the pellet ablatant is occurring toward the low field side edge of the plasma. New injection lines have been installed on the inner wall enabling injection from the highest field region of the device. Details of the results from injection at these different locations including comparisons with the measured pellet ablation light emission and the theoretical ablation rate will be presented. Modeling of the drift of the pellet ablatant following the ablation process will be discussed.

[GP01.100] Effect of Trapped Electrons and Collisionality on Electron Cyclotron Current Drive and Comparison with Experiments on the DIII--D Tokamak

Experiments on DIII--D have shown that the normalized figure of merit n_eI_pR/PT_e for Electron Cyclotron Current Drive is independent of minor radius.(T.C. Luce et al.), to be published in Proc.\ IAEA Meeting, Yokohama, Japan, 1998. This is surprising since trapping of current-carrying electrons is expected to reduce the driven current for off-axis deposition. However, theoretical treatments of the trapping effect have been based on the collisionless assumption at all energies. This assumption is clearly