Abstract
Twodimensional simulations with the BZOHAR[B. I. Cohen, B. F. Lasinski, A. B. Langdon, and E. A. Williams, Phys. Plasmas4, 956 (1997)] hybrid code (kinetic particle ions and Boltzmann fluid electrons) have been used to investigate the saturation of stimulated Brillouinbackscatter (SBBS) instability, including the effects of ionion collisions and inhomogeneity. Two types of Langevinoperator, ionion collision models were implemented in the simulations. In both models the collisions are functions of the local ion temperature and density, but the collisions have no velocity dependence in the first model. In the second model the collisions are also functions of the energy of the ion that is being scattered so as to represent a more physical FokkerPlanckcollision operator. Collisions decorrelate the ions from the acoustic waves in SBS, which disrupts ion trapping in the acoustic wave. Nevertheless, ion trapping leading to a hot ion tail and twodimensional physics that allows the SBS ion waves to nonlinearly scatter, remain important saturation mechanisms for SBBS in a highgain limit over a range of ion collisionality. Ionion collisions tend to increase ionwave dissipation, which decreases the gain exponent for stimulated Brillouinbackscattering; and the peak Brillouinbackscatterreflectivities decrease with increasing collisionality in the simulations for velocityindependent collisions and very weakly decrease for the range of FokkerPlanck collisionality considered. SBSbackscatter in the presence of a spatially nonuniform plasma flow is also investigated. Simulations show that, depending on the sign of the spatial gradient of the flow relative to the backscatter,ion trapping effects that produce a nonlinear frequency shift can enhance (autoresonance) reflectivities relative to antiautoresonant configurations, in agreement with theoretical arguments.
We gratefully acknowledge the many contributions to this effort and encouragement from Barbara Lasinski, Wally Manheimer, Richard Berger, Dustin Froula, Siegfried Glenzer, Denise Hinkel, Robert Kirkwood, Bill Kruer, Peter Rambo, Bert Still, and Larry Suter. This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under Contract No. W7405ENG48.
I. INTRODUCTION AND MOTIVATION
II. SIMULATION MODEL WITH IONION COLLISIONS
A. BZOHAR hybrid simulation model
B. Velocityindependent collision operator
C. FokkerPlanckcollision operator
III. STIMULATED BRILLOUIN SCATTERING WITH ION COLLISIONS
IV. SATURATION OF BRILLOUINBACKSCATTER WITH A FLOW GRADIENT
V. CONCLUSIONS
Key Topics
 Plasma waves
 57.0
 Fokker Planck equation
 41.0
 Reflectivity
 40.0
 Backscattering
 37.0
 Ion trapping
 35.0
Figures
(Color online) Preservation of a Maxwellian: comparison of evolved ion velocity distribution functions with no collisions (bcoll3) and with CIC collisions (bcoll10) showing that the Maxwellian is preserved and there is similar selfheating.
(Color online) Preservation of a Maxwellian: comparison of evolved ion velocity distribution functions with no collisions (bcoll3) and with CIC collisions (bcoll10) showing that the Maxwellian is preserved and there is similar selfheating.
Snapshots of and ion velocity distribution functions from collisionless simulations with no incident laser (bcoll17) and with incident laser and strong SBBS (bcem33n). Also shown is the relative growth of kinetic energy in bcoll17 versus the time step.
Snapshots of and ion velocity distribution functions from collisionless simulations with no incident laser (bcoll17) and with incident laser and strong SBBS (bcem33n). Also shown is the relative growth of kinetic energy in bcoll17 versus the time step.
Collisionless 2D simulation bcoll18 with no incident laser and with digital smoothing of the ion charge density: snapshots of the and ion velocity distribution functions and relative ion kinetic energy growth versus time step.
Collisionless 2D simulation bcoll18 with no incident laser and with digital smoothing of the ion charge density: snapshots of the and ion velocity distribution functions and relative ion kinetic energy growth versus time step.
Collisionless 2D simulation bcoll20 with fivepointstencil digital smoothing of the ion charge density and strong SBBS: snapshots of the and ion velocity distribution functions over regions centered at , , and , and integrated in .
Collisionless 2D simulation bcoll20 with fivepointstencil digital smoothing of the ion charge density and strong SBBS: snapshots of the and ion velocity distribution functions over regions centered at , , and , and integrated in .
(Color online) Relaxation of a strong temperature anisotropy: relative anisotropy versus time, and snapshots of the ion velocity distribution ( vs the square of velocities, and ).
(Color online) Relaxation of a strong temperature anisotropy: relative anisotropy versus time, and snapshots of the ion velocity distribution ( vs the square of velocities, and ).
(Color online) Padé approximations for the FokkerPlanck drag and perpendicular velocity variance diffusion coefficients vs compared to those calculated numerically from error functions.
(Color online) Padé approximations for the FokkerPlanck drag and perpendicular velocity variance diffusion coefficients vs compared to those calculated numerically from error functions.
Snapshots of the 3D ion velocity distribution function at and with and FokkerPlanck collisions preserving a Maxwellian (simulation bncoll3).
Snapshots of the 3D ion velocity distribution function at and with and FokkerPlanck collisions preserving a Maxwellian (simulation bncoll3).
FokkerPlanck collisional relaxation of a weak temperature anisotropy (initially and ) with and : relative temperature anisotropy versus dimensionless time using the same scales as in Fig. 5.
FokkerPlanck collisional relaxation of a weak temperature anisotropy (initially and ) with and : relative temperature anisotropy versus dimensionless time using the same scales as in Fig. 5.
Relaxation of an initially square velocity distribution function. Snapshots of ion velocity distribution functions from simulations with velocityindependent collisions (bcoll21) and FokkerPlanck collisions (bncoll6), and .
Relaxation of an initially square velocity distribution function. Snapshots of ion velocity distribution functions from simulations with velocityindependent collisions (bcoll21) and FokkerPlanck collisions (bncoll6), and .
Damping of an ion acoustic wave due to ion Landau damping and collisions for a collisionless simulation (bcoll30e) and a collisional simulation (bcoll30f, , ): mode amplitudes as functions of time at .
Damping of an ion acoustic wave due to ion Landau damping and collisions for a collisionless simulation (bcoll30e) and a collisional simulation (bcoll30f, , ): mode amplitudes as functions of time at .
(Color online) Peak and average SBBS reflectivities for parameters: , , , mass ratio, , and the Jones et al. collision model.
(Color online) Peak and average SBBS reflectivities for parameters: , , , mass ratio, , and the Jones et al. collision model.
SBS simulation bcoll26 with velocityindependent collisions and parameters: , , , real mass ratio for Be, , and instantaneous and average reflectivity, and ; reflected electromagnetic power spectrum versus time at and vs and time; power spectrum for vs and time. Here is the frequency of the SBBS ion acoustic wave.
SBS simulation bcoll26 with velocityindependent collisions and parameters: , , , real mass ratio for Be, , and instantaneous and average reflectivity, and ; reflected electromagnetic power spectrum versus time at and vs and time; power spectrum for vs and time. Here is the frequency of the SBBS ion acoustic wave.
(Color online) SBS simulation bcoll26 with velocityindependent collisions and parameters: , , , real mass ratio for Be, , and , Electromagnetic potential vs and at ; and velocity distribution functions on the left side of the domain at and 1200.
(Color online) SBS simulation bcoll26 with velocityindependent collisions and parameters: , , , real mass ratio for Be, , and , Electromagnetic potential vs and at ; and velocity distribution functions on the left side of the domain at and 1200.
(Color online) Peak and average SBBS reflectivities as functions of collisionality (FokkerPlanck collisions) and corresponding linear gain exponent for parameters: , , , mass ratio, , , and .
(Color online) Peak and average SBBS reflectivities as functions of collisionality (FokkerPlanck collisions) and corresponding linear gain exponent for parameters: , , , mass ratio, , , and .
SBBS instantaneous and cumulative timeaverage reflectivities versus time, power spectrum for versus and time, and power spectrum for reflected electromagnetic power versus and time, for parameters: , , , mass ratio, , , , FokkerPlanck collisions, and (bcoll26nn).
SBBS instantaneous and cumulative timeaverage reflectivities versus time, power spectrum for versus and time, and power spectrum for reflected electromagnetic power versus and time, for parameters: , , , mass ratio, , , , FokkerPlanck collisions, and (bcoll26nn).
(Color online) Absolute value of the electromagnetic potential at , ion velocity distribution functions and at , and 900 in simulation bcoll26nn for parameters: , , , mass ratio, , , , and FokkerPlanck collisions with .
(Color online) Absolute value of the electromagnetic potential at , ion velocity distribution functions and at , and 900 in simulation bcoll26nn for parameters: , , , mass ratio, , , , and FokkerPlanck collisions with .
Reflectivities as functions of time and power spectra for vs and time for parameters: , , , mass ratio, , , , the FokkerPlanck model (, bcoll28nn), and the Jones et al. model (, bcoll29s).
Reflectivities as functions of time and power spectra for vs and time for parameters: , , , mass ratio, , , , the FokkerPlanck model (, bcoll28nn), and the Jones et al. model (, bcoll29s).
Velocity distribution functions and on the left side of the domain at and 1050 for parameters: , , , mass ratio, , , , the FokkerPlanck model (, bcoll28nn), and the Jones et al. model (, bcoll29s).
Velocity distribution functions and on the left side of the domain at and 1050 for parameters: , , , mass ratio, , , , the FokkerPlanck model (, bcoll28nn), and the Jones et al. model (, bcoll29s).
(Color online) Peak and average reflectivities vs linear convective gain exponents for backscatter intensity with parameters: , , and 0.2, mass ratio, , collisionless, . data shown in red (autoresonant) above data shown in blue (antiautoresonant).
(Color online) Peak and average reflectivities vs linear convective gain exponents for backscatter intensity with parameters: , , and 0.2, mass ratio, , collisionless, . data shown in red (autoresonant) above data shown in blue (antiautoresonant).
SBBS instantaneous reflectivity and cumulative timeaverage reflectivity versus time, and power spectra plotted as functions of frequency and time for the reflected electromagnetic power at and , at and , and at and , for parameters: , , , mass ratio, , no collisions, and linear velocity gradient .
SBBS instantaneous reflectivity and cumulative timeaverage reflectivity versus time, and power spectra plotted as functions of frequency and time for the reflected electromagnetic power at and , at and , and at and , for parameters: , , , mass ratio, , no collisions, and linear velocity gradient .
Ion velocity distribution functions and at and 900 for simulation bgradv5d with linear velocity gradient showing the formation of a hot ion tail and transverse heating.
Ion velocity distribution functions and at and 900 for simulation bgradv5d with linear velocity gradient showing the formation of a hot ion tail and transverse heating.
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