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Register a new userPerpendicular diffusion coefficient of cosmic rays in the presence of weak adiabatic focusing
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The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past several authors have explored the influence of along-field adiabatic focusing on parallel diffusion of charged energetic particles. In this paper by using the Unified NonLinear Transport (UNLT) theory developed by Shalchi (SH2010) and the method of He and Schlickeiser (HS2014) we derive a new nonlinear perpendicular diffusion coefficient for non-uniform background magnetic field. This formula demonstrates that particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and weak adiabatic focusing limit the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For two-component model we simplify the perpendicular diffusion coefficient up to second order of the power series of adiabatic focusing characteristic quantity. We find that the first order modifying factor is equal to zero and the sign of the second one is determined by the energy of particles.
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It is very important to understand stochastic diffusion of energetic charged particles in non-uniform background magnetic field in plasmas of astrophysics and fusion devices. Using different methods considering along-field adiabatic focusing effect, various authors derived parallel diffusion coefficient $kappa_parallel$ and its correction $T$ to $kappa_{parallel 0}$, where $kappa_{parallel 0}$ is the parallel diffusion coefficient without adiabatic focusing effect. In this paper, using the improved perturbation method developed by He & Schlickeiser and iteration process, we obtain a new correction $T$ to $kappa_{parallel 0}$. Furthermore, by employing the isotropic pitch-angle scattering model $D_{mumu}=D(1-mu^2)$, we find that $T$ has the different sign as that of $T$. In this paper the spatial perpendicular diffusion coefficient $kappa_bot$ with the adiabatic focusing effect is also obtained.
We study the combined impact of magnetic mirroring and focusing on the ionization by cosmic rays (CRs) in dense molecular clouds and circumstellar disks. We show that for effective column densities of up to $sim10^{25}$ cm$^{-2}$ (where ionization is the main mechanism of energy losses by CRs) the two effects practically cancel each other out, provided the magnetic field strength has a single peak along field lines. In this case the ionization rate at a given location is controlled solely by attenuation of interstellar CRs due to energy losses. The situation is very different in the presence of magnetic pockets -- local minima of the field strength, where the CR density and thus ionization can be reduced drastically. We obtain simple analytical expressions allowing accurate calculation of the ionization rate in these regions.
Cosmic ray propagation is diffusive because of pitch angle scattering by waves. We demonstrate that if the high-amplitude magnetohydrodynamic turbulence with $tilde B/langle Brangle sim 1$ is present on top of the mean field gradient, the diffusion becomes asymmetric. As an example, we consider the vertical transport of cosmic rays in our Galaxy propagating away from a point-like source. We solve this diffusion problem analytically using a one-dimensional Markov chain analysis. We obtained that the cosmic ray density markedly differs from the standard diffusion prediction and has a sizable effect on their distribution throughout the galaxy. The equation for the continuous limit is also derived, which shows limitations of the convection-diffusion equation.
The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particles Larmor radius $R_L$ and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g., there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of order 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least $10^{6}$ times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to $10^{-2}lesssim R_L/l_c lesssim 10^{3}$, where $l_c$ is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for $R_L/l_c ll 1$, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.
Plasma outflow or wind against a gravitational potential under the influence of cosmic rays is studied in the context of hydrodynamics. Cosmic rays interact with the plasma via hydromagnetic fluctuations. In the process, cosmic rays advect and diffuse through the plasma. We adopt a multi-fluid model in which besides thermal plasma, cosmic rays and self-excited Alfven waves are also treated as fluids. We seek possible physically allowable steady state solutions of three-fluid (one Alfven wave) and four-fluid (two Alfven waves) models with given the boundary conditions at the base of the potential well. Generally speaking, there are two classes of outflows, subsonic and supersonic (with respect to a suitably defined sound speed). Three-fluid model without cosmic ray diffusion can be studied in the same way as the classic stellar wind problem, and is taken as a reference model. When cosmic ray diffusion is included, there are two categories of solutions. One of them resembles the three-fluid model without diffusion, and the other behaves like thermal wind at large distances when the waves wither and cosmic rays are decoupled from the plasma. We also inspect the effect of wave damping mechanisms (such as, nonlinear Landau damping). Roughly speaking, the effect is much smaller in supersonic outflow than in subsonic outflow.
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