User:Tomgibsonsandfield/Sandbox


 * $$f = n_D n_T \langle\sigma v\rangle = \frac{1}{4}n_e^2 \langle\sigma v\rangle $$


 * $$ P_{loss} = \frac{W}{\tau_E}$$


 * $$f E_{ch} \ge P_{loss}$$


 * $$f E_{ch} \ge \frac{W}{\tau_E}$$


 * $$\frac{1}{4}n_e^2 \langle\sigma v\rangle E_{ch} \ge \frac{W}{\tau_E}$$


 * $$ W = 3n_ek_BT$$


 * $$\frac{1}{4}n_e^2 \langle\sigma v\rangle E_{ch} \ge \frac{3n_ek_BT}{\tau_E}$$


 * $$\frac{1}{4}n_e \langle\sigma v\rangle E_{ch} \ge \frac{3k_BT}{\tau_E}$$


 * $$n_{\rm e} \tau_{\rm E} \ge \frac{12k_{\rm B}}{E_{\rm ch}}\,\frac{T}{\langle\sigma v\rangle}$$


 * $$\frac{T}{\langle\sigma v\rangle}$$


 * $$n_{\rm e} \tau_{\rm E}$$


 * $$n_D n_T$$


 * $$\sigma v$$


 * aA + bB ⇌ cC + dD