Collisionality: Difference between revisions
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Consider a test particle with charge ''q'', mass ''m'', and velocity ''v'' colliding with bulk particles with charge ''q*'', mass ''m*'', and thermal velocity ''v*''. Then the collision frequency ''ν = 1/τ<sub>coll</sub>'' is given by | Consider a test particle with charge ''q'', mass ''m'', and velocity ''v'' colliding with bulk particles with charge ''q*'', mass ''m*'', and thermal velocity ''v*''. Then the collision frequency ''ν = 1/τ<sub>coll</sub>'' is given by | ||
<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref> | <ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) {{ISBN|3540242171}}</ref> | ||
:<math>\nu = \left ( \frac{qq*n*}{\varepsilon_0 m}\right )^2 \frac{\ln \Lambda}{4\pi (m_r/m)v^3n*}</math> | :<math>\nu = \left ( \frac{qq^*n^*}{\varepsilon_0 m}\right )^2 \frac{\ln \Lambda}{4\pi (m_r/m)v^3n^*}</math> | ||
assuming ''v > v*'', where ''m<sub>r</sub> = mm*/(m+m*)'' is the reduced mass and ''n*'' the bulk particle density. | assuming ''v > v*'', where ''m<sub>r</sub> = mm*/(m+m*)'' is the reduced mass and ''n*'' the bulk particle density. | ||
The factor ln Λ appears due to the accumulation of many small-angle collisions within a Debye sphere. | The factor ln Λ appears due to the accumulation of many small-angle collisions within a [[Debye length|Debye sphere]]. | ||
== Dimensionless collisionality == | == Dimensionless collisionality == | ||
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<ref>[http://dx.doi.org/10.1088/0029-5515/39/12/301 ITER Physics Basis, Nucl. Fusion '''39''' (1999) 2137]</ref> | <ref>[http://dx.doi.org/10.1088/0029-5515/39/12/301 ITER Physics Basis, Nucl. Fusion '''39''' (1999) 2137]</ref> | ||
:<math>\nu* = \frac{\rm connection~length}{\rm trapped~particle~mean~free~path}</math> | :<math>\nu^* = \frac{\rm connection~length}{\rm trapped~particle~mean~free~path}</math> | ||
See [[Connection length]]. The mean free path is estimated by the thermal velocity divided by the collision frequency, ''v<sub>th</sub> / ν''. | |||
== References == | == References == | ||
<references /> | <references /> | ||
Latest revision as of 11:36, 26 January 2023
In a plasma, the collision time τcoll is defined as the time in which the trajectory of a (charged) particle undergoes a change of direction of 90 degrees. Due to the long range of the Coulomb force, Coulomb interactions are typically small angle scattering events, so that this direction change typically requires a large number of interactions.
Consider a test particle with charge q, mass m, and velocity v colliding with bulk particles with charge q*, mass m*, and thermal velocity v*. Then the collision frequency ν = 1/τcoll is given by [1]
assuming v > v*, where mr = mm*/(m+m*) is the reduced mass and n* the bulk particle density. The factor ln Λ appears due to the accumulation of many small-angle collisions within a Debye sphere.
Dimensionless collisionality
The dimensionless collisionality ν* is defined as [2]
See Connection length. The mean free path is estimated by the thermal velocity divided by the collision frequency, vth / ν.
References
- ↑ K. Miyamoto, Plasma Physics and Controlled Nuclear Fusion, Springer-Verlag (2005) ISBN 3540242171
- ↑ ITER Physics Basis, Nucl. Fusion 39 (1999) 2137