Plasma parameters: Difference between revisions

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<math display="block">\omega_{pi} = \left(\frac{4\pi n_i Z^2 e^2}{m_i}\right)^\frac{1}{2} \approx {1.32 \times 10^3} \,Z \left(\frac{n_i}{\mu}\right)^\frac{1}{2}\ \mbox{rad/s}</math>

| '''electron trapping rate''':

<math display="block">\nu_{Te} = \left(\frac{e E}{m_e}\right)^\frac{1}{2} \approx 7.26 \times 10^8\,E^\frac{1}{2}\ /\mboxmathrm{s^{-1}} </math>

| '''ion trapping rate''':

<math display="block">\nu_{Ti} = \left(\frac{Z e E}{m_i}\right)^\frac{1}{2} \approx {1.69 \times 10^7}\,\left(\frac{Z E}{\mu}\right)^\frac{1}{2}\ /\mboxmathrm{s^{-1}} </math>

| '''electron collision rate in completely ionized plasmas''':

<math display="block">\nu_e \approx 2.91 \times 10^{-6}\,\frac{n_e\ln\Lambda}{T_e^\frac{3}{2}}\ /\mboxmathrm{s^{-1}}</math>

| '''ion collision rate in completely ionized plasmas''':

<math display="block">\nu_i \approx 4.80 \times 10^{-8}\,\frac{Z^4 n_i\,\ln\Lambda}{\left(T_i^3 \mu\right)^\frac{1}{2}} \ /\mboxmathrm{s^{-1}}</math>

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In the study of [[tokamak]]s, '''collisionality''' is a [[dimensionless parameter]] which expresses the ratio of the electron-ion [[collision frequency]] to the [[banana orbit]] frequency.

The [[Plasma (physics)|plasma]] collisionality <math>\nu^*</math> is defined as<ref>{{ cite journal | author1 = ITER Physics Expert Group on Diagnostics | author2 = ITER Physics Basis | date = 1999 | title = Chapter 7: Measurement of plasma parameters | url = https://iopscience.iop.org/article/10.1088/0029-5515/39/12/307 | journal = Nuclear Fusion | volume = 39 | issue = 12 | pages = 2541–2575 | doi = 10.1088/0029-5515/39/12/307 | issn = 0029-5515 | url-access = subscription }}</ref><ref>{{ cite journal | last1 = Wenzel | first1 = K.W. | last2 = Sigmar | first2 = D.J. | date = 1990-06-01 | title = Neoclassical analysis of impurity transport following transition to improved particle confinement | url = https://iopscience.iop.org/article/10.1088/0029-5515/30/6/013 | journal = Nuclear Fusion | volume = 30 | issue = 6 |pages = 1117–1127 | doi = 10.1088/0029-5515/30/6/013 | issn = 0029-5515 | hdl = 1721.1/95018 | hdl-access = free | url-access = subscription }}</ref>

<math display="block">

\nu^* = \nu_\mathrm{ei} \, \sqrt{\frac{m_\mathrm{e}}{k_\mathrm{B} T_\mathrm{e}}} \, \varepsilon^{-\frac{3}{2}} \, qR,