Diferenças entre edições de "Magnetic mirrors / Fermi acceleration"
(Há 3 edições intermédias do mesmo utilizador que não estão a ser apresentadas) | |||
Linha 2: | Linha 2: | ||
A cosmic ray proton is trapped between two moving magnetic mirrors with | A cosmic ray proton is trapped between two moving magnetic mirrors with | ||
− | mirror ratio \(R_m=5\). Initially its energy is | + | 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 | + | 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, ''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. |
Edição atual desde as 15h53min 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, 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.