Landau Modes are Eigenmodes of Stellar Systems in the Limit of Zero Collisions

We consider the spectrum of eigenmodes in a stellar system dominated by gravitational forces in the limit of zero collisions. We show analytically and numerically using the Lenard–Bernstein collision operator that the Landau modes, which are not true eigenmodes in a strictly collisionless system (except for the Jeans unstable mode), become part of the true eigenmode spectrum in the limit of zero collisions. Under these conditions, the continuous spectrum of true eigenmodes in a collisionless system, also known as the Case–van Kampen modes, is eliminated. Furthermore, because the background distribution function in a weakly collisional system can exhibit significant deviations from a Maxwellian distribution function over long times, we show that the spectrum of Landau modes can change drastically even in the presence of slight deviations from a Maxwellian, primarily through the appearance of weakly damped modes that may be otherwise heavily damped for a Maxwellian distribution. Our results provide important insights for developing statistical theories to describe thermal fluctuations in a stellar system, which are currently a subject of great interest for N-body simulations as well as observations of gravitational systems.

Effects of Landau Damping and Collision on Stimulated Raman Scattering with Various Phase-Space Distributions

Stimulated Raman scattering (SRS) is one of the main instabilities affecting the success of the fusion ignition. Here, we study the relationship between Raman growth and Landau damping with various distribution functions combining the analytic formulas and Vlasov simulations. The Landau damping obtained by Vlasov-Poisson simulation and Raman growth rate obtained by Vlasov-Maxwell simulation are anti-correlated, which is consistent with our theoretical analysis quantitatively. Maxwellian distribution, flattened distribution, and bi-Maxwellian distribution are studied in detail, which represent three typical stages of SRS. We have also demonstrated the effects of plateau width, hot-electron fraction, hot-to-cold electron temperature ratio, and collisional damping on the Landau damping and growth rate. It gives us a deep understanding of SRS and possible ways to mitigate SRS through manipulating distribution functions to a high Landau damping regime.

Estimation of Electron Impact Ionization Rates of Li Using a Non-Maxwellian Distribution Function

We report an estimate of the cross-section and rate of electron-impact ionization of Li. The FAC code (Flexible Atomic Code) is used in order to determine the cross-section and to calculate the level of energy. We evaluate the effect of electron energy distribution functions on the measurement of the ionization rate for a non-Maxwellian energy distribution, if the fraction of hot electrons is small. In several types of plasma, it has been observed that certain (hot) electrons are governed by a non-Maxwellian energy distribution. These electrons affect the line spectra and other characteristics of plasma. By using a non-Maxwellian distribution of energies, we revealed the sensitivity of the electron-impact ionization rate of Li to types of the electron energy distribution and to the fraction of hot electrons.

Expansion of hot plasma with Kappa distribution in coronal flare sources

<p>We study how hot plasma that is released during a solar flare can be confined in its source and interact with surrounding colder plasma. The X-ray emission of coronal flare sources is well explained using Kappa velocity distribution. Therefore, we compare the difference in the confinement of plasma with Kappa and Maxwellian distribution. We use a 3D Particle-in-Cell code, which is large along magnetic field lines, effectively one-dimensional, but contains all electromagnetic effects. In the case with Kappa distribution, contrary to Maxwellian distribution, we found formation of several thermal fronts associated with double-layers that suppress particle fluxes. As the Kappa distribution of electrons forms an extended tail, more electrons are not confined by the first front and cause formation of multiple fronts. A beam of electrons from the hot part is formed at each front; it generates return current, Langmuir wave density depressions, and a double layer with a higher potential step than in the Maxwellian case. We compare the Kappa and Maxwellian cases and discuss how these processes could be observed.</p>

Simulating the Effects of Lower-Energy (<30 keV) Electrons on the Inner Magnetosphere Satellite Surface Charging Environment

&lt;p&gt;Satellite surface charging often occurs in the inner magnetosphere from the pre-midnight to the dawn sector when electron fluxes of&amp;#160; hundreds of eV to tens of keV are largely enhanced. Inner magnetosphere ring current models can be used to simulate/predict the satellite surface charging environment, with their flux outer boundary conditions specified either based on observations or provided by other models, such as MHD models. In the latter approach, the flux spectrum at the outer boundary is usually assumed to follow a Kappa or Maxwellian distribution, which however often departs greatly from, or underestimates, the realistic distribution below tens of keV, the energy range that is crucial in the spacecraft surface charging anomaly. This study aims to optimize the electron flux boundary condition of the inner magnetosphere ring current model to achieve a better representation of the surface charging environment. The MHD-parameterized flux spectrum is combined with an empirical electron flux model that specifies the &lt; 40 keV electron flux spectrum. New simulation results indicate that the surface charging environment, monitored by an integrated electron flux between 10&lt;E&lt;50 keV, is significantly enhanced by 1-2 orders of magnitude as opposed to the case in which Kappa/Maxwellian distribution is used at the outer boundary. The new results therefore show better agreement with Van Allen Probes measurements. The improved boundary condition also impacts the auroral precipitation, which may change the conductivity and circulated dynamics.&amp;#160;&lt;/p&gt;

TEST PARTICLE SIMULATIONS FOR NON-MAXWELLIAN PLASMA TRANSPORT: DISCRETIZED COLLISIONAL OPERATOR

The plasma observed in modern fusion devices is very often characterized by strongly non Maxwellian distribution function. That is the direct result of inevitable application of plasma heating techniques, such as neutral beam injection (NBI) and ion/electron cyclotron resonance frequency (ICRF/ECRF) heating, which induce the non Maxwellian fast ions. Another cause of transfer from Maxwellian to non Maxwellian is the reconnection of magnetic field lines followed by formation of magnetic resonant structures like magnetic islands and stochastic layers. One of the basic approaches used to simulate fusion plasma is test particle approach based on a solution of the equations of test particle motion. To make this approach more comprehensive one should take care of plasma particle interactions, i.e. Coulomb collisions in non Maxwellian environment. In present paper the expressions for the discretized collision operator of a general Monte Carlo equivalent form in terms of expectation values and standard deviation for an arbitrary non Maxwellian bulk distribution function are derived. The modification of transport coefficients of impurity ions caused by the transition from the background Maxwellian to non Maxwellian plasma is studied by means of this discretized collision operator. On this purpose, the set of monoenergetic neon test impurities is followed in a toroidal plasma consisting of bulk deuterons and electrons. The non Maxwellian distribution of the bulk is obtained by adding a fraction of energetic particles of the same species. It is demonstrated that a change of collision frequencies of impurities takes place in presence of this energetic fraction leading to a change of impurity neoclassical transport regime.