Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solution to a collisionless shallow-angle magnetic presheath with
  kinetic ions   Using a kinetic model for the ions and adiabatic electrons, we solve a steady
state, electron-repelling magnetic presheath in which a uniform magnetic field
makes a small angle $\alpha \ll 1$ (in radians) with the wall. The presheath
characteristic thickness is the typical ion gyroradius $\rho_{\text{i}}$. The
Debye length $\lambda_{\text{D}}$ and the collisional mean free path of an ion
$\lambda_{\text{mfp}}$ satisfy the ordering $\lambda_{\text{D}} \ll
\rho_{\text{i}} \ll \alpha \lambda_{\text{mfp}}$, so a quasineutral and
collisionless model is used. We assume that the electrostatic potential is a
function only of distance from the wall, and it varies over the scale
$\rho_{\text{i}}$. Using the expansion in $\alpha \ll 1$, we derive an
analytical expression for the ion density that only depends on the ion
distribution function at the entrance of the magnetic presheath and the
electrostatic potential profile. Importantly, we have added the crucial
contribution of the orbits in the region near the wall. By imposing the
quasineutrality equation, we derive a condition that the ion distribution
function must satisfy at the magnetic presheath entrance --- the kinetic
equivalent of the Chodura condition. Using an ion distribution function at the
entrance of the magnetic presheath that satisfies the kinetic Chodura
condition, we find numerical solutions for the self-consistent electrostatic
potential, ion density and flow across the magnetic presheath for several
values of $\alpha$. Our numerical results also include the distribution of ion
velocities at the Debye sheath entrance. We find that at small values of
$\alpha$ there are substantially fewer ions travelling with a large normal
component of the velocity into the wall.

35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat