Question

3 Magnetic Mirror Consider a magnetic mirror geometry with a magnetic field given by: $B = B_0 \left[ 1 + \left(\frac{z}{a_0}\right)^2 \right]$ (1) where $B_0 = 2.5T$ and $a_0 = 1.2m$. The center of the device is located at $z = 0$. The length of the mirror is 5 meters. (a) (1 point) Find the loss-cone pitch angle $\alpha_{LC}$ for the magnetic bottle. (b) (6 points) Consider a proton with kinetic energy of 1eV and a pitch angle of 15 deg at $z = 0$. Plot the following as a function of $z$: i. Magnetic field ii. Perpendicular velocity iii. Parallel velocity iv. Pitch angle v. Kinetic energy vi. Magnetic moment

          3 Magnetic Mirror
Consider a magnetic mirror geometry with a magnetic field given by:
$B = B_0 \left[ 1 + \left(\frac{z}{a_0}\right)^2 \right]$
(1)
where $B_0 = 2.5T$ and $a_0 = 1.2m$. The center of the device is located at $z = 0$. The length of the mirror
is 5 meters.
(a) (1 point) Find the loss-cone pitch angle $\alpha_{LC}$ for the magnetic bottle.
(b) (6 points) Consider a proton with kinetic energy of 1eV and a pitch angle of 15 deg at $z = 0$. Plot the
following as a function of $z$:
i. Magnetic field
ii. Perpendicular velocity
iii. Parallel velocity
iv. Pitch angle
v. Kinetic energy
vi. Magnetic moment

3 Magnetic Mirror
Consider a magnetic mirror geometry with a magnetic field given by:
B = B0 [ 1 + ((z)/(a0))^2 ]
(1)
where B0 = 2.5T and a0 = 1.2m. The center of the device is located at z = 0. The length of the mirror
is 5 meters.
(a) (1 point) Find the loss-cone pitch angle αLC for the magnetic bottle.
(b) (6 points) Consider a proton with kinetic energy of 1eV and a pitch angle of 15 deg at z = 0. Plot the
following as a function of z:
i. Magnetic field
ii. Perpendicular velocity
iii. Parallel velocity
iv. Pitch angle
v. Kinetic energy
vi. Magnetic moment

Added by Juan Francisco B.

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