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(Criou a página com "(F. F. ~ Chen 2.20) The magnetic field along the axis of a magnetic mirror is B(z)=B0(1+α2z2), where α is a constant. Suppose that at $z=0$ an electr...") |
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(F. F. ~ Chen 2.20) | (F. F. ~ Chen 2.20) | ||
The magnetic field along the axis of a magnetic mirror is B(z)=B0(1+α2z2), where α is | The magnetic field along the axis of a magnetic mirror is B(z)=B0(1+α2z2), where α is | ||
| − | a constant. Suppose that at | + | a constant. Suppose that at \(z=0\) an electron has velocity v2=3v2∥=32v2⊥. |
(a) Describe qualitatively the electron motion. | (a) Describe qualitatively the electron motion. | ||
| − | (b) Determine the values of | + | |
| + | (b) Determine the values of \(z\) where the electron is reflected. | ||
| + | |||
(c) Write the equation of motion of the guiding center for the direction parallel to →B and show that there is a | (c) Write the equation of motion of the guiding center for the direction parallel to →B and show that there is a | ||
sinusoidal oscillation. Calcule the frequency of the motion as a function of v. | sinusoidal oscillation. Calcule the frequency of the motion as a function of v. | ||
Edição atual desde as 16h58min de 17 de junho de 2017
(F. F. ~ Chen 2.20) The magnetic field along the axis of a magnetic mirror is B(z)=B0(1+α2z2), where α is a constant. Suppose that at z=0 an electron has velocity v2=3v2∥=32v2⊥.
(a) Describe qualitatively the electron motion.
(b) Determine the values of z where the electron is reflected.
(c) Write the equation of motion of the guiding center for the direction parallel to →B and show that there is a sinusoidal oscillation. Calcule the frequency of the motion as a function of v.