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z) = Bo(1+2)

z) = Bo(1+2)

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In order to confine a particle of charge q and mass m in a finite volume, a one-dimensional magnetic well is used (magnetic mirror), of magnitude given by: 72 B,(z) = Bo(1 +) L2 The total kinetic energy of the particle is "Ex". At the center of the magnetic well z=0, the velocity of the particle is oriented at some angle "a" with respect to the z-axis. Assuming that the particle's gyroradius is much less than L, derive an expression of the bounce frequency "o" as a function of the parameters provided, o = ob(L,a,Ek,m). Neglect the effects due to field line curvature. Please show all the required steps.
Transcribed Image Text:In order to confine a particle of charge q and mass m in a finite volume, a one-dimensional magnetic well is used (magnetic mirror), of magnitude given by: 72 B,(z) = Bo(1 +) L2 The total kinetic energy of the particle is "Ex". At the center of the magnetic well z=0, the velocity of the particle is oriented at some angle "a" with respect to the z-axis. Assuming that the particle's gyroradius is much less than L, derive an expression of the bounce frequency "o" as a function of the parameters provided, o = ob(L,a,Ek,m). Neglect the effects due to field line curvature. Please show all the required steps.
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