514:, 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.
500:
654:
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
226:
377:
717:
649:
825:
369:
258:
908:
Yamamoto, Naoto; Yamamoto, Masahiro; Kuwahara, Makoto; Sakai, Ryosuke; Morino, Takanori; Tamagaki, Kuniaki; Mano, Atsushi; Utsu, Akira; Okumi, Shouji; Nakanishi, Tsutomu (2007).
287:
94:
542:
316:
143:
589:
151:
655:
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
562:
114:
65:
495:{\displaystyle {\text{MTE}}=\int {\frac {\mathbf {p_{\perp }^{2}} }{2m}}f(\mathbf {p_{\perp }} ,\mathbf {p_{\parallel }} )\,dp_{\parallel }\,d^{2}p_{\perp }}
661:
877:
Bazarov, Ivan V.; Dunham, Bruce M.; Yulin, Li; Liu, Xianghong; Ouzounov, Dimitre G.; Sinclair, Charles K.; Hannon, Fay; Miyajima, Tsukasa (2008).
597:
728:
321:
27:(MTE) is a quantity that describes the variance of the transverse momentum of a beam. While the quantity has a defined value for any
910:"Thermal emittance measurements for electron beams produced from bulk and superlattice negative electron affinity photocathodes"
945:
234:
263:
70:
520:
292:
119:
879:"Thermal emittance and response time measurements of negative electron affinity photocathodes"
221:{\displaystyle {\text{MTE}}={\frac {1}{N}}\sum _{i}{\frac {\mathbf {p_{i,\perp }^{2}} }{2m}}}
567:
8:
20:
547:
510:
Emittance is a common quantity in beam physics which describes the volume of a beam in
99:
50:
921:
890:
852:
909:
878:
846:"Photocathodes for high brightness, high average current photoelectron injectors"
712:{\displaystyle \varepsilon _{\text{th}}={\sqrt {\frac {\text{MTE}}{m_{e}c^{2}}}}}
845:
939:
28:
644:{\displaystyle \varepsilon =\sigma _{x}{\sqrt {\frac {\text{MTE}}{mc^{2}}}}}
32:
820:{\displaystyle B_{n,4D}={\frac {m_{0}c^{2}\epsilon _{0}E_{0}}{2\pi MTE}}}
511:
925:
894:
722:
Likewise, the maximum brightness, or phase space density, is given by
856:
36:
364:{\displaystyle f(\mathbf {p_{\perp }} ,\mathbf {p_{\parallel }} )}
907:
318:. For a continuous, normalized distribution of particles
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844:Schmeißer, Martin Anton Helmut (11 December 2019).
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145:direction the mean transverse energy is given by
937:
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843:
471:
457:
31:, it is generally used in the context of
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253:{\displaystyle \mathbf {p_{\perp }} }
517:For a beam born with a spatial size
16:Accelerator physics energy quantity
13:
14:
957:
260:is the component of the momentum
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282:{\displaystyle \mathbf {p_{i}} }
273:
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89:{\displaystyle \mathbf {p_{i}} }
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544:and a 1-D MTE the minimum 2-D (
289:perpendicular to the beam axis
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1:
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116:traveling prominently in the
42:
506:Relation to Other Quantities
7:
537:{\displaystyle \sigma _{x}}
10:
962:
914:Journal of Applied Physics
883:Journal of Applied Physics
311:{\displaystyle {\hat {n}}}
138:{\displaystyle {\hat {n}}}
47:For a beam consisting of
67:particles with momenta
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25:mean transverse energy
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584:{\displaystyle p_{x}}
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946:Accelerator physics
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21:accelerator physics
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672:
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557:{\displaystyle x}
419:
384:
305:
216:
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132:
109:{\displaystyle m}
60:{\displaystyle N}
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591:) emittance is
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33:photoinjectors
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851:. p. 5.
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40:
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29:particle beam
26:
22:
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860:. Retrieved
839:
721:
653:
516:
509:
230:
46:
24:
18:
512:phase space
371:the MTE is
831:References
43:Definition
803:π
779:ϵ
667:ε
609:σ
602:ε
526:σ
488:⊥
467:∥
449:∥
434:⊥
401:⊥
390:∫
353:∥
338:⊥
303:^
245:⊥
198:⊥
175:∑
130:^
96:and mass
940:Category
37:electron
862:14 July
39:beams.
231:Where
23:, the
920:(2).
889:(5).
849:(PDF)
864:2022
564:and
35:for
922:doi
918:102
891:doi
887:103
853:doi
682:MTE
621:MTE
383:MTE
157:MTE
19:In
942::
916:.
912:.
885:.
881:.
671:th
928:.
924::
897:.
893::
866:.
855::
812:E
809:T
806:M
800:2
793:0
789:E
783:0
773:2
769:c
763:0
759:m
752:=
747:D
744:4
741:,
738:n
734:B
701:2
697:c
691:e
687:m
676:=
633:2
629:c
625:m
613:x
605:=
577:x
573:p
552:x
530:x
484:p
478:2
474:d
463:p
459:d
455:)
445:p
440:,
430:p
425:(
422:f
416:m
413:2
406:2
397:p
387:=
359:)
349:p
344:,
334:p
329:(
326:f
300:n
274:i
270:p
241:p
213:m
210:2
203:2
195:,
192:i
188:p
179:i
169:N
166:1
161:=
127:n
104:m
81:i
77:p
55:N
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