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(Criou a página com "(F. F. ~ Chen 2.20) The magnetic field along the axis of a magnetic mirror is \(B_(z) = B_0(1+\alpha^2z^2)\), where \(\alpha\) 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 \(B_(z) = B_0(1+\alpha^2z^2)\), where \(\alpha\) is
 
The magnetic field along the axis of a magnetic mirror is \(B_(z) = B_0(1+\alpha^2z^2)\), where \(\alpha\) is
a constant. Suppose that at $z=0$ an electron has velocity \(v^2 = 3 v_{\parallel}^2 = \frac{3}{2}v_{\perp}^2\).
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a constant. Suppose that at \(z=0\) an electron has velocity \(v^2 = 3 v_{\parallel}^2 = \frac{3}{2}v_{\perp}^2\).
  
 
(a) Describe qualitatively the electron motion.
 
(a) Describe qualitatively the electron motion.
(b) Determine the values of $z$ where the electron is reflected.
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(b) Determine the values of \(z\) where the electron is reflected.
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(c) Write the equation of motion of the guiding center for the direction parallel to \(\vec{B}\) and show that there is a
 
(c) Write the equation of motion of the guiding center for the direction parallel to \(\vec{B}\) 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 15h58min de 17 de junho de 2017

(F. F. ~ Chen 2.20) The magnetic field along the axis of a magnetic mirror is \(B_(z) = B_0(1+\alpha^2z^2)\), where \(\alpha\) is a constant. Suppose that at \(z=0\) an electron has velocity \(v^2 = 3 v_{\parallel}^2 = \frac{3}{2}v_{\perp}^2\).

(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 \(\vec{B}\) and show that there is a sinusoidal oscillation. Calcule the frequency of the motion as a function of \(v\).