# Considerations on ODR beam-size monitoring for gamma = 1000 beams Page: 2 of 5

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FERMILAB-CONF-08-108-AD

i

a

h"aC

350

300

2W0

200

150

100

BC

aa

12

z [m]

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 [9] 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

intensity as:impact parameter of 1250 pm. The beam size was 1375

pm by 200 pm [7]., : r

-s

D }15~

U

dI ( _I q2 C2

(u,C)= , -

do J2~ C v2 1 1

a 2N x

2ro2 27ro-,2* 200 100 0 OYUo 2oU

U x

IF, ~ cr i kr f:+ 1 2V'3-X LI[n be am e(1)

- - 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 anFigure 2: Calculated ODR image for a beam size of 1375

pm by 200 pm and an impact parameter starting at 1250

pm.

NUMERICAL RESULTS

The numerical integrations were done as described

previously at PAC07 [11]. 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___betaxm I

I I

- betY-r-------------------------- -------------

'I I

I I

' I

I r

- . IsoQI.

1211

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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 October 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.