Wave-particle equilibria with heavy ions in weakly collisional space plasmas

Abstract

Space plasmas are weakly collisional since characteristic time scales related to Coulomb collisions are much larger than those of Larmor gyration or wave--particle interactions. Thus, wave activity is likely to drive some of the non-thermal features that are observed in space plasma velocity distributions, such as temperature anisotropy, beams, and skewness. Therefore, we study how wave--particle interactions shape the velocity distribution functions of minor ions, and how these ions and their statistical properties modify the dispersion relation of electromagnetic waves. To achieve this, we derive the motion of heavy ions in electromagnetic waves using the Boris algorithm. We take the waves to be solutions of the fully kinetic dispersion relation of electromagnetic waves in two-ion component plasmas with parameters representative of the solar wind. We use the Arbitrary Linear Plasma Solver (ALPS) code to derive the linear Vlasov--Maxwell dispersion relation based on the actual distribution of the ions. The test-particles are initially in thermal equilibrium, and their distribution evolves due to interactions with the waves. By solving the dispersion relation using the evolved distributions, we show that the system evolves into a steady wave--particle equilibrium, which is characterized by a minimization of the interaction and energy transfer between wave and particles.

Figures (10)

• Figure 1: Real (left) and imaginary (center) parts of the frequency and collisionless heating rate (right) of A/IC waves with varying thermal speeds, given $T^{(\alpha)}/T^{(p)}=m^{(\alpha)}/m^{(p)}$ for different values of $v_{\text{th}}^{(\alpha)}$, and different number densities. When the solution splits into branches, we plot the one that is asymptotic to the A/IC solution at large wavenumbers with continuous lines, while we plot the remaining branch with dashed lines.
• Figure 2: Real (left) and imaginary (center) parts of the frequency and collisionless heating rate (right) of A/IC waves in an electron-proton-O$^{5+}$ with varying thermal speeds, given $T^{(\text{O}^{5+})}/T^{(p)}=m^{(\text{O}^{5+})}/m^{(p)}$ for different values of $\beta^{(p)}$, and different number densities.
• Figure 3: Results of the simulation for $\alpha$-particles (top panel), O$^{7+}$ ions (middle panel), and O$^{5+}$ ions (bottom panel), with initial thermal speeds of $\left(v_{\text{th}}^{(s)}/V_{A}^{(p)}\right)^2 =1.0$. We choose the number densities such that $\beta^{(s)}(t=0)=0.16$. The forcing wave has a normalized wavenumber of $ck/\omega_{p}^{(p)}=0.3$ and an amplitude of $|\delta B_y|(t=0)/B_0=2.5\times10^{-2}$. The left column displays the logarithmic difference $\Delta \log(f_0^{(s)})=\log(f_{\text{final}})-\log(f_{\text{initial}})$ of the test-particles' final and initial VDFs for heavy ions; continuous contours are isocontours of the initial (black) and final (yellow) VDFs, dashed contours indicate curves of constant $\Delta \log(f)=\pm0.01,\pm0.10$, and vertical dash-dotted lines indicate the $\ell=0$ and $\ell=1$ resonances in Equation \ref{['eq:resonance']}. The center column shows the mean kinetic-to-thermal energy ratio of the test-particles as a function of time. The right column shows $\beta_{\perp}$ (blue) and $\beta_{\parallel}$ (red), as well as the temperature anisotropy $T_{\perp}/T_{\parallel}$ (green) as functions of time.
• Figure 4: Logarithmic difference of the final and initial $\alpha$-particle VDFs near the cyclotron-resonant velocity for $ck/\omega_{p}^{(p)}=0.3$ and $|\delta B_y|/B_0 = 2.5\times 10^{-2}$ at different stages of the simulation. Contours of the initial and evolved VDFs are plotted in black and yellow lines, respectively. Dashed cyan lines represent shells of constant energy in the wave-frame, given by $(v_{\parallel}-\omega_{\mathrm r}/k_{\parallel})^2+v_{\perp}^2=\text{constant.}$
• Figure 5: Mean field-aligned velocity and heat flux for $\left(v_{\text{th}}^{(\text{O}^{5+})}/V_{A}^{(p)}\right)^2=0.1$ for O${}^{5+}$ ions with different concentrations, forced by A/IC waves of the upper and lower branch. Continuous (dashed) curves indicate forcing by a wave with of amplitude $|\delta B_y|/B_0=5.0\times 10^{-2}$ ( $|\delta B_y|/B_0=2.5\times 10^{-2}$).