Mean transverse energy

In accelerator physics, the mean transverse energy (MTE) is a quantity that describes the variance of the transverse momentum of a beam. While the quantity has a defined value for any particle beam, it is generally used in the context of photoinjectors for electron beams.[1]

Definition

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For a beam consisting of   particles with momenta   and mass   traveling prominently in the   direction the mean transverse energy is given by

 

Where   is the component of the momentum   perpendicular to the beam axis  . For a continuous, normalized distribution of particles   the MTE is

 

Relation to Other Quantities

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Emittance is a common quantity in beam physics which describes the volume of a beam in phase space, and is normally conserved through typical linear beam transformations; for example, one may transition from a beam with a large spatial size and a small momentum spread to one with a small spatial size and a large momentum spread, both cases retaining the same emittance. Due to its conservation, the emittance at the species source (e.g., photocathode for electrons) is the lower limit on attainable emittance.

For a beam born with a spatial size   and a 1-D MTE the minimum 2-D (  and  ) emittance is[2]

 

The emittance of each dimension may be multiplied together to get the higher dimensional emittance. For a photocathode the spatial size of the beam is typically equal to the spatial size of the ionizing laser beam and the MTE may depend on several factors involving the cathode, the laser, and the extraction field. Due to the linear independence of the laser spot size and the MTE, the beam size is often factored out, formulating the 1-D thermal emittance[3]

 

Likewise, the maximum brightness, or phase space density, is given by

 

References

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  1. ^ Schmeißer, Martin Anton Helmut (11 December 2019). "Photocathodes for high brightness, high average current photoelectron injectors" (PDF). p. 5. doi:10.18452/20481. Retrieved 14 July 2022.
  2. ^ Bazarov, Ivan V.; Dunham, Bruce M.; Yulin, Li; Liu, Xianghong; Ouzounov, Dimitre G.; Sinclair, Charles K.; Hannon, Fay; Miyajima, Tsukasa (2008). "Thermal emittance and response time measurements of negative electron affinity photocathodes". Journal of Applied Physics. 103 (5). doi:10.1063/1.2838209.
  3. ^ Yamamoto, Naoto; Yamamoto, Masahiro; Kuwahara, Makoto; Sakai, Ryosuke; Morino, Takanori; Tamagaki, Kuniaki; Mano, Atsushi; Utsu, Akira; Okumi, Shouji; Nakanishi, Tsutomu (2007). "Thermal emittance measurements for electron beams produced from bulk and superlattice negative electron affinity photocathodes". Journal of Applied Physics. 102 (2). doi:10.1063/1.2756376.