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Electron hole instability as a primordial step towards sustained intermittent turbulence in linearly subcritical plasmas

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Electron hole instability as a primordial step towards sustained intermittent turbulence in linearly subcritical plasmas
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Electron and ion holes are highly stable nonlinear structures met omnipresently in driven collisionless hot plasmas. A mechanism destabilizing small perturbations into holes is essential for an often witnessed but less understood subcritically driven intermittent plasma turbulence. In this paper we show how a tiny, eddy-like, non-topological electron seed fluctuation can trigger an unstable evolution deep in the linearly damped region, a process being controlled by the trapping nonlinearity and hence being beyond the realm of the Landau scenario. After a (transient) transition phase modes of the privileged spectrum of cnoidal electron and ion holes are excited which in the present case consist of a solitary electron hole (SEH), two counter-propagating 'Langmuir' modes (plasma oscillation), and an ion acoustic mode. A quantitative explanation involves a nonlinear dispersion relation with a forbidden regime and the negative energy character of the SEH, properties being inherent in Schamel's model of undamped Vlasov–Poisson structures identified here as lowest order trapped particle equilibria. An important role in the final adaption of nonlinear plasma eigenmodes is played by a deterministic response of trapped electrons which facilitates transfer of energy from electron thermal energy to an ion acoustic nonuniformity, accelerating the SEH and positioning it into the right place assigned by the theory.
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Transcript: English(auto-generated)
Here I am going to explain the abstract of our paper in the New Journal of Physics with the title, Electron hole instability as a primordial step towards sustained intermittent turbulence in linearly subcritical plasmas. Before going into details, I want to explain what is particle trapping in a wave.
In the figure A, the particle denoted by a red dot having kinetic energy lesser than the potential energy of the wave will bounce back and forth in the wave and that's why it is called trapped particle and the particle denoted by blue dot having kinetic energy greater than the potential energy of the wave can move freely that's why this particle is called free particle. Figure B presents their phase phase diagram.
Electron and ion holes are trapped particle nonlinearity generated highly stable coherent structure with reduced phase phase density at trapped particle orbit and are frequently observed in collisionless plasmas and they are an important agent in intermittent plasma turbulence. Linear Blasov theory of plasma neglects this fundamental trapped particle nonlinearity
and recovers only the free plasma modes and they cannot explain the existence of trapped particle nonlinearity generated coherent structures therefore it questions their validity in collisionless plasma turbulence theory. Subcritical regime of plasma and they are important in turbulence.
According to the linear theory of plasma in a current driven plasma below a critical dip value between electron and ion, linear plasma modes never be unstable. The dip values below this critical value is called subcritical regime of plasma. Most of the turbulence theory is based on the evolution of these linear plasma
modes and their subcritical limit. Since the linear theory does not incorporate the trapped particle nonlinearity, this turbulence theory cannot explain the collisionless intermittent plasma turbulence properly. Therefore a mechanism destabilizing small perturbation into a hole is essential to an often witnessed but less understood subcritical driven intermittent plasma turbulence.
In this paper we show how a tiny eddy like electron phase phase sheet fluctuation which is equivalent to a background fluctuation in any hot plasma can trigger an unstable evolution in the subcritical regime and finally generate a stable electron hole. For the first time we have quantitatively identified an unstable forbidden region of
electron holes and in this forbidden region they help to exchange the thermal energy of free electrons with ions. This result will help for formulating a better model of turbulent plasma.
This is a time evolution plot for electron phase space and electron ion density for a current driven plasma. In this case the drift value is 0.01 which is well inside the subcritical regime. The initial perturbation of the electron distribution function is chosen at velocity location 0.004 which is marked with a white line.
After transient phase the initial perturbation accelerates to velocity location 0.034 and finally an electron hole is excited which is the solution of a nonlinear dispersion relation where k0 is the wave vector, zr is the principal part of the plasma dispersion function, v0 and u0 is the velocity of the electron hole in the electron and ion
frame, theta is the temperature ratio and beta is the trap particle parameter for electron and psi is the amplitude of the potential and the energy of the electron hole is given by delta w. Two important characteristics of stable electron hole is the left hand side of the nonlinear
dispersion function is always be greater than 0 and the energy of the electron hole is less than 0 and depending upon these two characteristics of a electron hole we have identified a forbidden unstable region for the electron hole.
In the figure A we plotted the left hand side of the distribution nonlinear dispersion relation with time and in the plot region 1 and 2 is the unstable region only the region 3 is a stable region. The improper shielding of electric field associated with the perturbation causes acceleration to higher velocity
until it is perfectly shielded and the figure B presents during this unsealeded evolution thermal energy of free electrons transferred to the ion thermal energy and this exchange mechanism is mediated by the electron hole. Therefore in this paper we have presented a new scenario of plasma
turbulence which is also in contrast to the related 2D compressible shear flow dynamics such as plane Cote flow for which such a detailed analysis is not available. Thank you