Magnetic Field Dependence of the Amplification of Sound by Conduction Electrons

A Boltzmann equation technique is used to calculate the magnetic field dependence of sound, amplified by interaction with conduction electrons in the presence of crossed dc electric and magnetic fields. It is shown that both geometric resonances and cyclotron resonances can be found under conditions of amplification. This occurs when the electron-drift velocity in the crossed fields, $v_H$, has a component in the direction of propagation of sound which exceeds the sound velocity $v_s$. The geometric resonances occur under the same conditions as in zero electric field, but the cyclotron resonances are Doppler shifted and occur for $\omega -\mathrm{q}·{\mathrm{v}}_H=n{\omega }_c$.