Beam temperature

In physics, the beam temperature describes the width of the velocity distribution in a particle beam .

A longitudinal temperature (in the direction of beam propagation) and a transverse temperature (perpendicular to it) are defined: ${\displaystyle T_{\|}}$ ${\displaystyle T_{\bot }}$

${\displaystyle T_{\|}={\frac {1}{2}}{\frac {m_{\text{Teilchen}}\cdot \operatorname {Var} (v_{\|})}{k_{\mathrm {B} }}}}$

${\displaystyle T_{\bot }={\frac {m_{\text{Teilchen}}\cdot \operatorname {Var} (v_{\bot })}{k_{\mathrm {B} }}}}$

This is the variance of the velocity distribution in the corresponding direction, m _{particles is} the mass of the particles in the beam and k _{B is} the Boltzmann constant . ${\displaystyle \operatorname {Var} (v)}$

The variance only indicates the dispersion of the speed as the central moment , not its mean value. Specifically, in the co-moving reference system , in which the average value disappears, the variance is simply the mean square speed: . ${\displaystyle \operatorname {Var} (v_{\|/\bot })=\langle v_{\|/\bot }^{2}\rangle }$

The beam temperature can also be understood as a measure of the phase space density of the beams. Especially when a particle beam is cooled, the phase space density is increased for lower velocities, since the particles occupy a narrower velocity range after cooling (smaller variance of the distribution).

See also

• Electron cooling
• Stochastic cooling
• Zeeman slower

literature

• J. Dietrich: Jet cooling . In: Manfred von Ardenne, Gerhard Musiol, Uwe Klemradt (ed.): Effects of physics and their applications . Harri Deutsch Verlag, 2005, ISBN 978-3-8171-1682-9 , pp. 139–145, 143 ( limited preview in Google Book search).