Explain the role of plasma physics in understanding the behavior of ionized gases and its applications in fusion energy and space physics.
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Plasma is often referred to as the fourth state of matter, alongside solids, liquids, and gases. Show more…
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What is a plasma? Distinguish between magnetic and inertial confinements. Why is confinement such a problem for fusion?
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A plasma is a gas of ionized (charged) particles. When plasma is in motion, magnetic effects "squeeze" its volume, inducing inward pressure known as a pinch. Consider a cylindrical tube of plasma with radius $R$ and length $L$ moving with velocity $\overrightarrow{\boldsymbol{v}}$ along its axis. If there are $n$ ions per unit volume and each ion has charge $q,$ we can determine the pressure felt by the walls of the cylinder. (a) What is the volume charge density $\rho$ in terms of $n$ and $q ?(b)$ The thickness of the cylinder "surface" is $n^{-1 / 3}$. What is the surface charge density $\sigma$ in terms of $n$ and $q$ ? (c) The current density inside the cylinder is $\vec{J}=\rho \overrightarrow{\boldsymbol{v}}$ Use this result along with Ampere's law to determine the magnetic field on the surface of the cylinder. Denote the circumferential unit vector as $\hat{\phi} .$ (d) The width of a differential strip of surface current is $R d \phi .$ What is the differential current $d I_{\text {surface }}$ that flows along this strip? (e) What differential force is felt by this strip due to the magnetic field generated by the volume current? (f) Integrate to determine the total force on the walls of the cylinder, then divide by the wall area to obtain the pressure in terms of $n, q, R,$ and $v .(\mathrm{g})$ If a plasma cylinder with radius $2.0 \mathrm{~cm}$ has a charge density of $8.0 \times 10^{16}$ ions $/ \mathrm{cm}^{3},$ where each ion has a charge of $e=1.6 \times 10^{-19} \mathrm{C}$ and is moving axially with a speed of $20.0 \mathrm{~m} / \mathrm{s}$, what is its pinch pressure?
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