Question

a r PLASMA B? I VACUUM Figure 9.3. A plasma equilibrium in which a uniform plasma fills all space except for an evacuated cylindrical hole produced by a current-carrying conductor (see Problem 9.1). Problem 9.1: A plasma of uniform pressure $p$ fills all of space except for an evacuated infinitely long cylindrical 'hole' of radius $a$, which is produced by a conductor carrying a current $I$ placed on the axis of the cylindrical hole. The conductor produces an azimuthal field $B_\theta$, as shown in Figure 9.3. Show that the maximum radius of the vacuum hole that can be created in equilibrium in this way is given by $a^2 = \mu_0 I^2 / 8\pi^2 p$. Is there a $z$-directed current in the plasma? What is its magnitude and where is it located?

          a
r
PLASMA
B?
I
VACUUM
Figure 9.3. A plasma equilibrium in which a uniform plasma fills all space except for an
evacuated cylindrical hole produced by a current-carrying conductor (see Problem 9.1).
Problem 9.1: A plasma of uniform pressure $p$ fills all of space except
for an evacuated infinitely long cylindrical 'hole' of radius $a$, which is
produced by a conductor carrying a current $I$ placed on the axis of the
cylindrical hole. The conductor produces an azimuthal field $B_\theta$, as shown
in Figure 9.3. Show that the maximum radius of the vacuum hole that can
be created in equilibrium in this way is given by $a^2 = \mu_0 I^2 / 8\pi^2 p$. Is there
a $z$-directed current in the plasma? What is its magnitude and where is it
located?

a
r
PLASMA
B?
I
VACUUM
Figure 9.3. A plasma equilibrium in which a uniform plasma fills all space except for an
evacuated cylindrical hole produced by a current-carrying conductor (see Problem 9.1).
Problem 9.1: A plasma of uniform pressure p fills all of space except
for an evacuated infinitely long cylindrical 'hole' of radius a, which is
produced by a conductor carrying a current I placed on the axis of the
cylindrical hole. The conductor produces an azimuthal field Bθ, as shown
in Figure 9.3. Show that the maximum radius of the vacuum hole that can
be created in equilibrium in this way is given by a^2 = μ0 I^2 / 8π^2 p. Is there
a z-directed current in the plasma? What is its magnitude and where is it
located?

Added by Tyler L.

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