scholarly journals Effect of a weak ion collisionality on the dynamics of kinetic electrostatic shocks

2019 ◽  
Vol 85 (1) ◽  
Author(s):  
Andréas Sundström ◽  
James Juno ◽  
Jason M. TenBarge ◽  
István Pusztai
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Boundary Layers ◽  
Analytical Model ◽  
Electrostatic Potential ◽  
Charge Balance ◽  
Ion Distribution ◽  
Partial Reflection ◽  
Collisionless Regime

In strictly collisionless electrostatic shocks, the ion distribution function can develop discontinuities along phase-space separatrices, due to partial reflection of the ion population. In this paper, we depart from the strictly collisionless regime and present a semi-analytical model for weakly collisional kinetic shocks. The model is used to study the effect of small but finite collisionalities on electrostatic shocks, and they are found to smooth out these discontinuities into growing boundary layers. More importantly, ions diffuse into and accumulate in the previously empty regions of phase space, and, by upsetting the charge balance, lead to growing downstream oscillations of the electrostatic potential. We find that the collisional age of the shock is the more relevant measure of the collisional effects than the collisionality, where the former can become significant during the lifetime of the shock, even for weak collisionalities.

Orbit Tomography of energetic particle distribution functions

2021 ◽  
Author(s):  
Luke Stagner ◽  
William W Heidbrink ◽  
Mirko Salewski ◽  
Asger Schou Jacobsen ◽  
Benedikt Geiger
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Energetic Particle ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Velocity Space ◽  
Space Distribution ◽  
Weight Functions ◽  
Ion Distribution ◽  
Fast Ions

Abstract Both fast ions and runaway electrons are described by distribution functions, the understanding of which are of critical importance for the success of future fusion devices such as ITER. Typically, energetic particle diagnostics are only sensitive to a limited subsection of the energetic particle phase-space which is often insufficient for model validation. However, previous publications show that multiple measurements of a single spatially localized volume can be used to reconstruct a distribution function of the energetic particle velocity-space by using the diagnostics' velocity-space weight functions, i.e. Velocity-space Tomography. In this work we use the recently formulated orbit weight functions to remove the restriction of spatially localized measurements and present Orbit Tomography, which is used to reconstruct the 3D phase-space distribution of all energetic particle orbits in the plasma. Through a transformation of the orbit distribution, the full energetic particle distribution function can be determined in the standard {energy,pitch,r,z}-space. We benchmark the technique by reconstructing the fast-ion distribution function of an MHD-quiescent DIII-D discharge using synthetic and experimental FIDA measurements. We also use the method to study the redistribution of fast ions during a sawtooth crash at ASDEX Upgrade using FIDA measurements. Finally, a comparison between the Orbit Tomography and Velocity-space Tomography is shown.

scholarly journals Phase space effects on fast ion distribution function modeling in tokamaks

2016 ◽  
Vol 23 (5) ◽  
pp. 056106 ◽  
Author(s):  
M. Podestà ◽  
M. Gorelenkova ◽  
E. D. Fredrickson ◽  
N. N. Gorelenkov ◽  
R. B. White
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Ion Distribution ◽  
Fast Ion ◽  
Space Effects

scholarly journals Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Alessandro Geraldini
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Electrostatic Potential ◽  
Grazing Angle ◽  
Debye Length ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Ion Temperature ◽  
Ion Distribution ◽  
Orbit Model

A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field $\boldsymbol {B}$ inclined at a small angle, $\alpha \ll 1$ (in radians), to the target. Adiabatic electrons are assumed, requiring $\alpha \gg \sqrt {Zm_{e}/m_{i}}$ , where $m_{e}$ and $m_{i}$ are the electron and ion mass, respectively, and $Z$ is the charge state of the ion. An electric field $\boldsymbol {E}$ is present to repel electrons, and so the characteristic size of the electrostatic potential $\phi$ is set by the electron temperature $T_{e}$ , $e\phi \sim T_{e}$ , where $e$ is the proton charge. An asymptotic scale separation between the Debye length $\lambda _{D} = \sqrt {\epsilon _0 T_{{e}} / e^{2} n_{{e}} }$ , the ion sound gyro-radius $\rho _{s} = \sqrt { m_{i} ( ZT_{e} + T_{i} ) } / (ZeB)$ and the size of the collisional region $d_{c} = \alpha \lambda _{\textrm {mfp}}$ is assumed, $\lambda _{D} \ll \rho _{s} \ll d_{c}$ . Here $\epsilon _0$ is the permittivity of free space, $n_{e}$ is the electron density, $T_{i}$ is the ion temperature, $B= |\boldsymbol {B}|$ and $\lambda _{\textrm {mfp}}$ is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances $x$ from the wall such that $\rho _{s} \ll x \ll d_{c}$ , that is, collisions are not treated. A self-consistent solution of the electrostatic potential for $x \sim \rho _{s}$ is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of $\phi (x)$ and results in an analytical expression for the ion distribution function at the target. It assumes that $\tau =T_{i}/(ZT_{e})\gg 1$ , and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For $\tau \gtrsim 1$ , the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.

Sloshing ion distribution function in a minimum B mirror field

2005 ◽  
Vol 12 (2) ◽  
pp. 022504 ◽  
Author(s):  
O. Ågren ◽  
N. Savenko
Keyword(s):  
Distribution Function ◽  
Ion Distribution

scholarly journals On Boundedness of Entropy of Photon Gas in Noncommutative Spacetime

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Kazi Ashraful Alam ◽  
Mir Mehedi Faruk
Keyword(s):  
Black Holes ◽  
Distribution Function ◽  
Phase Space ◽  
Partition Function ◽  
Boltzmann Distribution ◽  
Einstein Distribution ◽  
Entropy Bound ◽  
Photon Gas ◽  
Noncommutative Spacetime ◽  
Bose Einstein

Entropy bound for the photon gas in a noncommutative (NC) spacetime where phase space is with compact spatial momentum space, previously studied by Nozari et al., has been reexamined with the correct distribution function. While Nozari et al. have employed Maxwell-Boltzmann distribution function to investigate thermodynamic properties of photon gas, we have employed the correct distribution function, that is, Bose-Einstein distribution function. No such entropy bound is observed if Bose-Einstein distribution is employed to solve the partition function. As a result, the reported analogy between thermodynamics of photon gas in such NC spacetime and Bekenstein-Hawking entropy of black holes should be disregarded.

scholarly journals Relativistic transformation of phase-space distributions

2011 ◽  
Vol 29 (7) ◽  
pp. 1259-1265 ◽  
Author(s):  
R. A. Treumann ◽  
R. Nakamura ◽  
W. Baumjohann
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Volume Element ◽  
Plasma Parameters ◽  
Astrophysical Plasmas ◽  
Relativistic Case ◽  
Phase Space Volume ◽  
Radiation Theory ◽  
High Mach ◽  
Space Volume

Abstract. We investigate the transformation of the distribution function in the relativistic case, a problem of interest in plasma when particles with high (relativistic) velocities come into play as for instance in radiation belt physics, in the electron-cyclotron maser radiation theory, in the vicinity of high-Mach number shocks where particles are accelerated to high speeds, and generally in solar and astrophysical plasmas. We show that the phase-space volume element is a Lorentz constant and construct the general particle distribution function from first principles. Application to thermal equilibrium lets us derive a modified version of the isotropic relativistic thermal distribution, the modified Jüttner distribution corrected for the Lorentz-invariant phase-space volume element. Finally, we discuss the relativistic modification of a number of plasma parameters.

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