Education/ExperimentMenu/1stLevelBasic/ElectronEnergyConfinementTime/FlowChartSimple/fig/latex.txt
$I_{ch} (t)$
$\overline{R_{ch}}\approx\frac{U_l (t)}{I_{ch} (t)}$
$I_{ch+p} (t)$
$1.1\cdot 10^7$ A/V
$\int_0^t$
$\overline{I_p}=<I_p(t)>_{t_1}^{t_2}$
$\overline{U_l}=<U_l(t)>_{t_1}^{t_2}$
$\overline{n_e}=<n_e(t)>_{t_1}^{t_2}$
$\overline{R_p}=\frac{\overline{U_l}}{\overline{I_p}}$
$\overline{P_{OH}}=\overline{R_p}\cdot \overline{I_p}^2$
$\overline{T_{e}(0)}=0.9\cdot\overline{R_p}^{-2/3}$
$\frac{d W_p(t)}{dt}=0$
$\frac{d W_p(t)}{dt}|_{t_1}^{t_2}=0$
$(\frac{d W_p(t)}{dt}=0)$
$\overline{P_{loss}}=\overline{P_{OH}}$
$\overline{W_p}=\overline{V_p}\cdot\frac{\overline{n_e}\cdot k_B\cdot\overline{T_{e}(0)}}{3}$
$\overline{\tau_E}=\frac{\overline{W_p}}{\overline{P_{loss}}}$
$\overline{\tau_{eE}}=\frac{\overline{W_p}}{\overline{P_{loss}}}$
$\overline{V_p}=(80 \pm 10)$ l
${V_p}=(57 \pm 5)$ l
$eV=1.602\cdot 10^{-19}$ J
$R_p=\frac{U_l}{I_p}$
$P_{OH}=R_p\cdot I_p^2$
$T_{e}(0)=0.9\cdot R_p^{-2/3}$
$\frac{d W_p(t)}{dt}=0$
$\frac{d W_p(t){dt}|_{t_1}^{t_2}=0$
$(\frac{d W_p(t){dt}=0)$
$P_{loss}=P_{OH}$
$W_p=V_p\cdot\frac{n_e\cdot k_B\cdot T_{e}(0)}{3}$
$W_p=V_p\cdot\frac{n_e\cdot k_B\cdot (T_{e}(0)\cdot eV)}{3}$
$\tau_E=\frac{W_p}{P_{loss}}$
$\tau_{eE}=\frac{W_p}{P_{loss}}$
$V_p}=(80 \pm 10)$ l