2022 Summer EC500 SB1 Midterm
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2022 Summer EC500 SB1 Midterm
(Problem 1) (20 points)
An electron moves in a magnetic mirror, having mass me, kinetic energy εe, and a pitch angle ec at the mid-plane where the magnetic field intensity is Bo . Find (1) the electron cyclotron frequency and (2) its gyro-radius at the mid-plane. If this electron can be confined in the magnetic mirror, find (3) the electron parallel velocity at the mid-plane, and (4) the magnetic field Bm in the vicinity of the mirror coils.
(Problem 2) (30 points)
O-Mode-produced Langmuir waves (LWs), initially propagating along the constant background magnetic field, beat with the pre-existing lower hybrid waves, to become obliquely propagating LWs. (1) Explain why the beat waves with the sum frequency are expected to have much higher intensity than the beat waves with the difference frequency. (2) Set up the wave frequency and wave vector matching conditions, to represent this nonlinear scattering process, and (3) discuss the
difference between this phenomenon and a parametric instability process.
(Problem 3) (18 points)
A laser beam with a radius ro propagates from air into a uniform, collisional plasma. This EM wave beam can heat the plasma throughout its path. Assuming that plasma heating is the dominant process to consider, discuss how this EM wave-plasma
interactions will change the plasma density and the shape of the EM wave
(Problem 4) (32 points)
Suppose that an intense whistler wave at 30 KHz excites lower hybrid waves and zero-frequency mode via four-wave interactions. (1) Use a schematic together with corresponding wave frequency and wave vector matching condition, to illustrate these processes. If the local electron plasma frequency and the electron cyclotron frequency are 6 MHz and 1 MHz, respectively, calculate (2) the wave length of this whistler wave, (3) the phase velocity, and (4) the group velocity of the whistler wave.
2022-08-01