The Plasma Containment Crisis · AI Generator #GEN-1CD9A1C4
Physics · thermodynamics
Problem
A fusion research facility uses magnetic confinement to contain a plasma of deuterium ions at temperature T=2.0×108K. The plasma is initially contained in a cylindrical chamber of radius R0=1.5m and length L=6.0m at pressure P0=105Pa. Due to a magnetic field instability, the confinement suddenly fails and the plasma begins to expand adiabatically into a much larger evacuated chamber of total volume Vf=500m3. The plasma behaves as an ideal gas with γ=5/3 (monatomic). During this expansion, some of the plasma's thermal energy is converted to kinetic energy of directed motion. When the plasma reaches the chamber walls, what is the speed v of the plasma flow? Assume the plasma remains at sufficiently high temperature that it stays ionized throughout the process. The mass of a deuterium ion is mD=3.34×10−27kg.