Classical physics impossibility of magnetic fusion reactor with neutral beam injection at thermonuclear energies below 200 KeV.

Lawson criterion was specifically derived for inertial fusion and DT gas of stable lifetime without ions and magnetic fields$^{1}$. It was revised with realistic parametrers$^{2}$. To account for the losses of unstable ions against neutralization with lifetime $\tau $, $n\left( t \right)=n\tau \left[ 1-exp\left( \raise0.7ex\hbox{${-t}$} \!\mathord{\left/ {\vphantom {{-t} \tau }}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$\tau $} \right) \right]\to n\tau \, \mathrm{for}\, \tau \ll t$, where $\tau ^{-1}=n_{0}[ERR:md:MbegChr=0x2329,MendChr=0x232A,nParams=1] $, $n_{0}=\, $residual gas density. Second revised criterion becomes: $ntL={10}^{14}{\mathrm{cm}}^{\mathrm{-3}}\mathrm{s},\, tL=$ Lawson conf. time becomes $n\tau tL={10}^{14}\, \mathrm{or}\, ntL={10}^{16}/\tau $. In CT resonance regime below critical energy To, $\tau \sim {10}^{-5}$, and Lawson requirement $nt_{L}\sim {10}^{21}$ i.e. not realistic. Luminosity (reaction rate for $\sigma =1)$ is that of two unstable particles each with lifetime $\tau $: $L=n^{2}\left( t \right)v_{12}=n^{2}t^{2}v_{12}$. In subcritical regime, $L={10}^{-10}n^{2}\, \mathrm{for}\, n={10}^{14}{\mathrm{cm}}^{\mathrm{-3}},\, v\sim {10}^{9}\mathrm{cm\, }\mathrm{s}^{\mathrm{-1}}=L={10}^{27}$. . Which is negligible and implies a negative power flow reactor. But above $T_{0},\, \mathrm{at}\, T_{D}=725\mathrm{\, KeV},\, \tau =20s$ was observed implying $L={10}^{39}$ i.e. massive fusion energy production$^{3,4}$. 1. Lawson, Proc. Phys. Soc. B70, 6 (1957) 2. Maglich Miller, J. App. Phys. 46, 2916 [Fig. 13] (1975); 3. Phys. rev lett.54, 769 (1985); 4. NIM A271 pp. 1-128 (34 papers)