\(r_{ e }=\cfrac { m_{ e }\pm \sqrt { m^{ 2 }_{ e }-\cfrac { A }{ \pi v^{ 2 } } (\cfrac { q^{ 2 } }{ \varepsilon _{ o } } -\cfrac { T_{ e }T_{ n } }{ \tau _{ o } } ) } }{ 2A } \)
\( r_{ e }=\cfrac { m_{ e }\pm \sqrt { m^{ 2 }_{ e }-\cfrac { A }{ \pi v^{ 2 } } \cfrac { q^{ 2 } }{ \varepsilon _{ o } } +\cfrac { A }{ \pi v^{ 2 } } \cfrac { T_{ e }T_{ n } }{ \tau _{ o } } } }{ 2A } \) --- (*)
Should \(r_e\) decrease or increase with increasing \(T\) given that \(A\) also decreases?
If \(r_e\) increases with \(T\) in gerenal then plasma needs another explanation.
From (*)
\(r_{ e }=\cfrac { m_{ e } }{ 2A } \pm \sqrt { \cfrac { m^{ 2 }_{ e } }{ 4A^{ 2 } } -\cfrac { 1 }{ 4A\pi v^{ 2 } } \cfrac { q^{ 2 } }{ \varepsilon _{ o } } +\cfrac { 1 }{ 4A\pi v^{ 2 } } \cfrac { T_{ e }T_{ n } }{ \tau _{ o } } } \)
We see that the lower valued root of \(r_e\) decreases but the higher valued root increases. The spread of the two roots about the double root point \(\cfrac{m_e}{2A}\), increases.
Plasma can result if we push the electron further into the nucleus using a rectified voltage waveform (from the post "Rectified Waveform To The Rescue") at higher temperature. This is the reverse of pushing the electron into the conduction band. Goggles please.
The higher valued root above the kink does not guarantee that the material become more conductive lest the electron loses a packet of energy and transit to the conduction band over the kink point.
