Abstract
Due to Landau resonant interaction with lower hybrid waves in the lower hybrid current drive scheme part of electrons are accelerated and, as a result of this, a tail of energetic electrons is formed on the electron distribution function. The same situation takes place in the problem of type III radio bursts when the suprathermal burst electrons acquire a plateau distribution due to excitation of plasma waves in the solar wind plasma. These distributions are unstable with respect to the cyclotron excitation of waves at anomalous Doppler resonance (“fan” instability). In this case, the tail electrons interact simultaneously with both (i) waves that accelerate or decelerate them (Čerenkov resonance) and (ii) waves excited in the process of the fan instability that led to their pitch angle diffusion. Because velocity diffusion lines of electrons formed due to heir interaction with each type of waves intersect, this interaction can lead not only to pitch angle diffusion but also to heating of electrons mainly in perpendicular direction. We investigated this mechanism of electron heating and studied the temporal evolution of the electron temperature and the energy of excited waves. Our results show significant enhancement of the electron perpendicular temperature due to this stochastic heating mechanism.
The authors are grateful to the reviewer and the editor for a number of important remarks and suggestions. The NASA Grant No NNX09AG95G is acknowledged for support of this study.
I. INTRODUCTION
II. EQUATIONS: SOLUTION
III. DISCUSSION
IV. CONCLUSION
Key Topics
 Plasma waves
 37.0
 Cumulative distribution functions
 12.0
 Diffusion
 10.0
 Electron beams
 8.0
 Plasma instabilities
 8.0
H05H1/02
Figures
Electrons interacting at Landau resonance (1) with oblique Langmuir or lower hybrid waves diffuse along the dashed lines. After falling in resonance with lower hybrid wave packets (phase speed ), resonant interaction at anomalous Doppler resonance (5) makes them move along the solid circles. The overall motion of electrons simultaneously interacting with wave packets through different resonances (Čerenkov and cyclotron) is not just diffusion in pitch angle but stochastic diffusion in perpendicular velocity (or in energy) as well.
Electrons interacting at Landau resonance (1) with oblique Langmuir or lower hybrid waves diffuse along the dashed lines. After falling in resonance with lower hybrid wave packets (phase speed ), resonant interaction at anomalous Doppler resonance (5) makes them move along the solid circles. The overall motion of electrons simultaneously interacting with wave packets through different resonances (Čerenkov and cyclotron) is not just diffusion in pitch angle but stochastic diffusion in perpendicular velocity (or in energy) as well.
Contour plots of the electron distribution function formed when electrons interact simultaneously with both types of waves through two types of resonance (Čerenkov and cyclotron) The snapshots are taken at t = 0, 6, 152, 278, 308, 325, 358, 404 (from left to right then top to bottom). All velocities are in units of initial plasma thermal velocity with logarithmic rescaling of contour levels.
Contour plots of the electron distribution function formed when electrons interact simultaneously with both types of waves through two types of resonance (Čerenkov and cyclotron) The snapshots are taken at t = 0, 6, 152, 278, 308, 325, 358, 404 (from left to right then top to bottom). All velocities are in units of initial plasma thermal velocity with logarithmic rescaling of contour levels.
Contour plots of the electron distribution function when interactions at Landau and cyclotron resonances are modeled separately. Cyclotron electronwave interaction was switched on after interaction at Landau resonance that created the plateau was switched off. The snapshots are taken at t = 152, 265, 300, 306, 311, 431 . All velocities are in units of initial plasma thermal velocity with logarithmic rescaling of contour levels.
Contour plots of the electron distribution function when interactions at Landau and cyclotron resonances are modeled separately. Cyclotron electronwave interaction was switched on after interaction at Landau resonance that created the plateau was switched off. The snapshots are taken at t = 152, 265, 300, 306, 311, 431 . All velocities are in units of initial plasma thermal velocity with logarithmic rescaling of contour levels.
Temporal dynamics of the wave energy, kinetic energy of electrons, and electron perpendicular temperature for the dense beam case ( ). The lower panel corresponds to the case of simultaneous resonance interactions shown in Figure 2 and the upper panel corresponds to the second case when resonant interactions of electrons with waves were treated independently (Figure 3 ). The total energy is conserved in both cases rather well, but internal distribution of energy is strikingly different, with twice as much energy channeled into perpendicular motions of electrons when both types of resonant interactions are working in concert. (Energy is in units of initial plasma kinetic energy of single degree of freedom).
Temporal dynamics of the wave energy, kinetic energy of electrons, and electron perpendicular temperature for the dense beam case ( ). The lower panel corresponds to the case of simultaneous resonance interactions shown in Figure 2 and the upper panel corresponds to the second case when resonant interactions of electrons with waves were treated independently (Figure 3 ). The total energy is conserved in both cases rather well, but internal distribution of energy is strikingly different, with twice as much energy channeled into perpendicular motions of electrons when both types of resonant interactions are working in concert. (Energy is in units of initial plasma kinetic energy of single degree of freedom).
Temporal dynamics of the wave energy, kinetic energy of electrons, and electron perpendicular temperature for the case of sparse beam ( ). The lower panel corresponds to the case of simultaneous resonance interactions and the upper panel corresponds to the case when resonant interactions of electrons with waves were treated independently. Again, as for the dense beam, the total energy is conserved in both cases rather well, but internal distribution of energy is strikingly different, with twice as much energy channeled into perpendicular motions of electrons when both types of resonant interactions are working in concert. (Energy is in units of initial plasma kinetic energy of single degree of freedom).
Temporal dynamics of the wave energy, kinetic energy of electrons, and electron perpendicular temperature for the case of sparse beam ( ). The lower panel corresponds to the case of simultaneous resonance interactions and the upper panel corresponds to the case when resonant interactions of electrons with waves were treated independently. Again, as for the dense beam, the total energy is conserved in both cases rather well, but internal distribution of energy is strikingly different, with twice as much energy channeled into perpendicular motions of electrons when both types of resonant interactions are working in concert. (Energy is in units of initial plasma kinetic energy of single degree of freedom).
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