Transport and diffusion of particles due to transverse drift waves

Abstract

Transport and diffusion of plasma particles perpendicular and parallel to the magnetic field is discussed in the framework of the transverse drift wave theory. The starting model includes the density and magnetic field gradients perpendicular to the magnetic field vector. In such an inhomogeneous environment the transverse drift wave naturally develops. The transverse drift wave is a low frequency mode, with the frequency far below the ion gyro-frequency, it is driven by these gradients and it propagates perpendicular to them. The mode is also purely perpendicular to the magnetic field and it is electromagnetically transverse, which implies that when its wave vector is perpendicular to the magnetic field vector, the perturbed electric field is along the equilibrium magnetic field, while in the same time the perturbed magnetic field is in the direction of the background gradients. In application to the solar wind, it is shown that very small wave electric field amplitude, of the order of 10 −7 V/m, within one wave period can produce the drift of protons in both directions, perpendicular to the ecliptic plane and also along the background magnetic field, to distances measured in millions of kilometers. The electric field along the magnetic field vector implies particle acceleration in the same direction. When a critical threshold velocity of the particle is achieved, the particle motion becomes stochastic. This is a completely new nonlinear stochastic mechanism which follows from the very specific geometry of the transverse drift mode. Particle drift perpendicular to the magnetic field vector means a diffusion of particles, with the effective diffusion coefficient for ions that is at least 11 orders of magnitude larger than the classic diffusion coefficient. The features of this diffusion are: within certain time interval, initially faster particles will diffuse to larger distances, and the same holds for protons in comparison to heavier ions. For electrons the effective diffusion coefficient can easily match the one obtained from observations, i.e., to become of the order of 10 17 m 2 /s. It is also expected that the wave-induced stochastic motion will considerably increase the effective collision frequency in such an environment which is, with respect to its mean parameters, practically collision-lees. Hence, the solar wind regions affected by such a stochastic acceleration may show various unexpected features that are typical for collisional plasmas.

Drift wave stabilized by an additional streaming ion or plasma population

“…Using the identity Λ n (x) = Λ −n (x) and the expansion of the plasma dispersion function for n = 0 terms in limit of the large argument, and assuming the realistic low frequency case for both the components, i.e., ξ nf i , ξ nsi 1 and ω Ω (s,f )i , respectively, one can easily prove that the n = 0 terms vanish from the last terms of Eqs. (1)(2)(3)(4) and we get the dispersion relation…”

“…α denotes the species, q α is their charge, n α0 is the equilibrium density, L nsα is the inhomogeneity scale length of static component and ω = ω − k z v α0 is the Doppler shifted frequency due to the streaming velocity v α0 . We are considering the case of low plasma beta β α = 2µ 0 n α0 T α /B 2 0 << 1 due to which the magnetic field gradient is ignored following the relation L nsα /L Bsα ∼ β α [3], where L Bsα is the scale length of magnetic field inhomogeneity. The parallel integration gives rise to the plasma dispersion function W ( ξ n(s,f )α ) with the argument ξ n(s,f )α , where the perpendicular integration yields the modified Bessel function in the term Λ n (b (s,f )α ) = e −b (s,f )α I n (b (s,f )α ) with the argument b (s,f )α .…”

“…The wave is self-excited and it grows due to the free energy in plasma inhomogeneity and this remains so even in plasmas with hot ions. This fact was used in our recent papers where a new paradigm was put forward for the heating of the solar corona [1,2] and solar wind [3] by drift waves, based on stochastic heating mechanism from Refs. [4,5].…”

Energy in density gradient

“…For example, in the presence of a magnetic field the radial density gradient, or pressure gradient in general, may be counteracted by the magnetic pressure. This in principle implies the presence of the radial inhomogeneity of the magnetic field as well, which can be small in case of a small plasmabeta, 15,16 yet in any case it is supposed to balance the assumed pressure (density) gradient. But quite generally, the quasi-static equilibrium may be described through the balance of forces…”

New features of ion acoustic waves in inhomogeneous and permeating plasmas

“…Hence, if observed flux of such a wave is too low or absent, its role in the heating is assumed as unimportant. However, wave heating scenario may include models with waves that are generated directly on the spot, i.e., in the corona itself and then dissipated contributing to heating, see examples based on the drift wave theory presented in Vranjes and Poedts ([25,26,28,29]) and in Vranjes ( [30], [31]). This implies the presence of some energy source for excitation of such waves directly in the corona.…”