Diferenças entre edições de "Magnetic mirrors / Fermi acceleration"
| Linha 4: | Linha 4: | ||
mirror ratio \(R_m=5\). Initially its energy is \(W=1\) keV and \(v_\perp = v_\parallel\) at the midplane. | mirror ratio \(R_m=5\). Initially its energy is \(W=1\) keV and \(v_\perp = v_\parallel\) at the midplane. | ||
Each mirror moves toward the midplane with a velocity \(v_m=10\) km/s and the initial distance between the mirrors is \(L=10^{10}\) km. | Each mirror moves toward the midplane with a velocity \(v_m=10\) km/s and the initial distance between the mirrors is \(L=10^{10}\) km. | ||
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| + | (a) Using the invariance of \(\mu\), find the energy to which the proton is accelerated before it escapes. | ||
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| + | (b) How long does it take to reach that energy? Suggestions: i) suppose that the $B$ field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, \textit{i.e.}, treat each mirror as a flat piston and show that the velocity gained at each bounce is \(2v_m\); ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably | ||
| + | during the acceleration process. | ||
Revisão das 15h52min de 17 de junho de 2017
(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).
A cosmic ray proton is trapped between two moving magnetic mirrors with mirror ratio \(R_m=5\). Initially its energy is \(W=1\) keV and \(v_\perp = v_\parallel\) at the midplane. Each mirror moves toward the midplane with a velocity \(v_m=10\) km/s and the initial distance between the mirrors is \(L=10^{10}\) km.
(a) Using the invariance of \(\mu\), find the energy to which the proton is accelerated before it escapes.
(b) How long does it take to reach that energy? Suggestions: i) suppose that the $B$ field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, \textit{i.e.}, treat each mirror as a flat piston and show that the velocity gained at each bounce is \(2v_m\); ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably during the acceleration process.