End Loss from a High-Beta Plasma Column

The previous theoretically predicted diverging confinement time of a high-$\beta$ linear sharp plasma column as $\beta \to 1$ is removed by including the magnetic tension effect near the column throats. This result explains our own simulation as well as those of Brackbill, Menzel, and Barnes, and is in good agreement with experimental values. The confinement time $\tau$ of a plasma with thickness $a$ and length $L$ at $\beta =1\mathrm{}$ is found to be $\tau =\frac{3}{4}{\left(\frac{3}{2\pi }\right)}^{\frac{1}{2}}\left(\frac{L}{2c_S}\right){\left(\frac{L}{a}\right)}^{\frac{1}{2}}$.