Temperature Control in Radiatively Cooled Plasmas through Autoresonant Drive of TG-waves

We demonstrate accurate temperature control of pure electron plasmas, using driven wave heating ``autoresonantly'' in balance with cyclotron cooling. The $m_{\theta } =0$ Trivelpiece-Gould wave frequencies are temperature-dependent, as$f_{TG} (T)=f_{TG} (0)\ast [1+\varepsilon T]$; and they exhibit a narrow Lorentzian absorption response $R(f)$ with width $\gamma \sim 10^{-3}f_{TG} $. A continuous drive amplitude $A_{dr} $ then produces plasma heating power $P_{h} \propto A_{dr}^{2} R(f_{dr} )$, which can exactly balance the cyclotron cooling power$P_{c} \propto T \mathord{\left/ {\vphantom {T {\tau_{c} }}} \right. \kern-\nulldelimiterspace} {\tau_{c} }$. This balance point is autoresonantly \textit{stable} when $f_{dr} \approx f_{TG} (T)-\gamma $: if $T$ increases, then $f_{TG} (T)$ also increases and $f_{dr} $ gets further from resonance, so the heating power decreases and $T$ decreases back to the balance point. (The second power-balance point at $f_{dr} \approx f_{TG} (T)+\gamma $ is \textit{unstable}.) In practice, we use a $m_{z} =3$ TG wave having frequency range $5.2