Considerations on ODR beam-size monitoring for gamma = 1000 beams Page: 2 of 5
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Figure 1: Lattice functions (case 2 waist at z~ 1 m) for the NML Downstream beamline with the proposed three-station
configuration indicated by the arrows (lattice plot courtesy of Mike Church, Fermilab).
near field based on the method of virtual quanta described
by Jackson  in dealing with the photon-like fields of
relativistic beams. One convolves the electron beam's
Gaussian distribution of sizes 6- and o- with the field
expected from a single electron at point P in the metal
plane. One wishes to calculate the incoherent sum of
radiation from all beam particles in a pulse emitted from a
given point on the ODR radiator, i.e. at u = P - ro, where
P is the field point with respect to the origin and ro is the
position of the beam centroid with respect to the origin.
The impact parameter is b = u - r, where r = r(x,y)
denotes a position in the beam measured from the beam
centroid. One then can write the differential spectral
impact parameter of 1250 pm. The beam size was 1375
pm by 200 pm .
, : r
dI ( _I q2 C2
(u,C)= , -
do J2~ C v
2 1 1
a 2N x
* 200 100 0 OYUo 2oU
IF, ~ cr i kr f:+ 1 2V'3-X LI[n be am e
- - Y
ffdxdyK2 (ab)e 2e 2,,
where o = radiation frequency, v = particle velocity ~ c =
speed of light, q = electron charge, N is the particle
number, a = 1/yk, and K,(ab)= K, (u, - x)2 + (U, - y
is a modified Bessel function. Since one measures light
intensity I, this should be proportional to IEx12 + lEy12,
resulting in the K, dependence. The incoherent photon
intensity is proportional to N, the number of electrons, in
contrast to the case of coherent diffraction radiation in the
far infrared (FIR), which is enhanced by N2.
The APS experiments actually started with a single
plane which was inserted vertically. We evaluated the
beam size parallel to the single edge. In Fig. 2 we show a
calculation of the signal distribution in the optical near
field based on this new model for a 7-GeV beam at an
Figure 2: Calculated ODR image for a beam size of 1375
pm by 200 pm and an impact parameter starting at 1250
The numerical integrations were done as described
previously at PAC07 . In this case the parameters
were adjusted to assess the y=1000 regime, initially for
approximately 500-MeV electrons that are anticipated in
the NMVL at Fermilab. In this case a superconducting linac
would be combined with a high-average-current photo
injector. Under the scenario of a single semi-infinite metal
plane inserted from above the beam axis, we assessed the
ODR monitor beam-size sensitivity at a value centered at
200 pm. In Fig. 3 we show both the parallel (px) and
perpendicular (py) components of the ODR profiles for a
series of impact parameters. For this beam size near 200
m and impact parameters, the near-field ODR parallel
- betY-r-------------------------- -------------
- . I
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Lumpkin, A.H.; /Fermilab; Yao, C.-Y.; /Argonne; Chiadroni, E.; Castellano, M. et al. Considerations on ODR beam-size monitoring for gamma = 1000 beams, article, April 1, 2008; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc900483/m1/2/: accessed December 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.