R. B. Fiorito,

 R. B. Fiorito Co., Silver Spring, MD. 20901

A. Shkvarunets, and P. O'Shea,

University of Maryland, College Park, MD 20742

Abstract

Optical Transition Radiation (OTR) interferometry has been shown to be a useful diagnostic to measure the divergence of electron beams with energies in the range of 15-100 MeV. A limitation of this method is due to beam scattering in the first foil of the interferometer. To mitigate this undesirable effect we propose to use a perforated first foil in the interferometer. In this case a substantial fraction of the unscattered beam electrons passing through the holes will produce Optical Diffraction Radiation (ODR). The total radiation produced from the first and second foils will be coherent ODR and OTR from unscattered electrons and incoherent ODR and OTR from heavily scattered electrons in the first foil. A successful ODR-OTR interferometer willbe generally useful to measure the divergence of low emittance beams which can be presently measured using conventional OTR interferometry and would be very useful for low energy low emittance beam diagnostics, for example for the University of Maryland's Infrared Free Electron Laser (MIRFEL) 10 MeV accelerator.We are proposingODR-OTR interferometry be used to measure the divergence of the ATF 30 MeV accelerator, which has nearly ideal parameters for an initial proof of principle experiment.

1 Introduction

OTR interferometry is a proven method for measuring the rms emittances of relativistic electron beams with energies ranging from 15-100 MeV [1]. In this technique two parallel thin foils, oriented at 45 degrees with respect to the electron beam, produce forward and backward directed OTR. When the distance between the foils is comparable to the vacuum coherence length L ~ g²l , interference fringes are observed whose visibility is a function of the rms beam divergence.

Scattering in the first foil of the interferometer limits this method to beam energies above about 10 MeV. When the energy of the electron beam falls below about 10 MeV and the rms divergence of the beam is smaller than about 0.05/g, mso-fareast-font-family:Arial'>it becomes very difficult to design a foil with less scattering than the divergence of the beam. To overcome this limitation, we plan to use a perforated first foil as shown in Figure 1. The total output light intensity distribution observed is the coherent sum of the intensities of ODR and OTR produced by the unscattered and scattered portions of the beam.

By proper choice of the first foil thickness, the inter-foil spacing, the size, number and spacing of the holes and the band pass of the imaging optics, interference fringes from the unscattered electrons can be seen above the background light produced from the scattered portion of beam. The rms divergence of the unperturbed beam can be measured from the visibility of the interference fringes. In addition, the orthogonal (x, y) components of the divergence can be separately obtained by observing polarized interferences when the beam is focused to either an x or y waist condition [1].

 

Figure 1:Schematic of ODR-OTR interferometer

2 approach

In order to design the ODR-OTR interferometer to be sensitive to a given expectedbeam divergence we have developed two computer codes:Code (1) calculates the ODR and OTR intensity distributions produced by unscattered (U) and scattered (S) beams as shown in Figure 2.

 

 

 

 

Figure 2:An expanded view of one of the foil cells

  Code (2) calculates the coherent addition of ODR and OTR radiation fields produced at foils 1 and 2 by beams (U) and beam (S) which are assumed to have divergences divergences s_U, and s_S, respectively.

 

2.1 Optical Diffraction Radiation - Code (1)

Following Ter-Mikelian [2] we assume that the optical diffraction radiation produced by electrons passing through the perforated foil can be calculated by applying Huygens Principle to the virtual photon field accompanying each electron (Weizsäcker-Williams method of virtual quanta). The virtual photons are scattered or diffracted by the circular hole and produce real photons at a screen downstream from the foil.The distribution of the field from the electrons at this screen is then given by the Huygens Fresnel Integral

 

 

 

whereU_x,yis any field component, k=/c, R is the distance from S_f, the differential element of area of the foil and u_x,y is the Fourier component of the free space radial field of the electron given by:

 

 

 

where a = w/(gv), v is the electron velocity and K₁ is the Hankel function with imaginary argument.

2.2 ODR - OTR Interferences - Code (2)

Code (2) calculates the total x or y component of the two foil light intensity distribution given by:

 

where>I_n,B = S( E_ne,B)²/2 are the x or y intensity components from foils n = 1,2 for beams B = U, S;E_neare the x or y components of the radiation field for a single electron produced by foils 1 and 2 calculated usingCode (1);and

where d is the spacing between the foils, b =v/c,q_eis the electron trajectory angle within the beam and q is the observation angle.

 

 

The effect of beam divergence on the interference intensity pattern is taken into account by numerically convolving the intensity given above in Eq. (1) with a Gaussian distribution of electron angles:

line'>  

 If>s_x,y<< g^-1, the angle of peak emission for OTR and ODR, then the radiation fields at the observation planeE_{1,2 e} (s_x,y,q_x,y) are slowly varying functions of q _x,yand hence are nearly independent of the beam divergences x,y.Then only the phase term will be sensitive to beam divergence. The presence of beam divergence produces a reduction in the interference fringe visibility.

 

3 Computational results

3.1 Code (1) Results

The Results of Code (1) are presented in Fig. 3 the ATF 30 MeV beam . A perforation ratio (area of holes to foil area) of 0.8 was used. Code (1) was tested in cases for which theoretical formulas for ODR were available Refs. [2-4], and found to be in excellent agreement with the theoretical calculations in all cases.

 

 

 

 

 

 

 

Figure 3: ODR and OTR intensities from the first and second foils for the unscattered, and scattered portions of the beam passing through foils 1 and 2.

 

3.2.Code (2) Results

The results of Code 2 are given in Figs 4, 5 and 6. The observation wavelength l = 650 nm, the bandpass Dl/l= 0.01 and the beam divergence due to scattering in foil 1, s_S=10 mrads. Under these conditions the OTR produced by the scattered beam is essentially incoherent and forms a background above which the interference fringes from the unscattered beam are visible. The effects of unscattered beam divergences s_U= 0.01 – 0.3 mrad are shown.

Figure 4:The effect of divergence on the total intensity of ODR-OTR for a two foil interferometer, whose foils are separated by d = 70 mm.The presence of fringes indicates a coherent addition of intensities from the first and second foils.The resulting fringe patterns for various divergences in the range of expected beam value are shown.

4 experiment

 

The experiment proposed for ATF is

 

(1)     to use conventional OTR interferometry to measure the beam divergenceand

 

(2)     to compare the results of the divergence measurements using (1) to that obtained using ODR-OTR interferometry.\

 

Conventional OTRI and ODR-OTRI can be both be done by using a common fixed distance two foil system, with part of the first foil containing a small (several beam diameters) perforated section.

 

One, multiple position actuator will be used to expose the beam to three positions different sections on the first foil:

 

a)        a cut away section, which will allow the beam to pass through without generating any forward direction OTR or ODR from the first foil; this sectuib will allow us to optically align the interferometer with the help of an upstream laser which is available on the ATF beam line

b)              a solid section of the first foil which will be used to generate conventional two foil OTRI

c)              a perforated area on the first foil which will be used to generate ODR-OTRI .

 

  The second foil, which will be a mirrored surface, is parallel and at fixed distance (35-70 mm) with respect to the first foil. The actuator and foils will be housed in a six inch cube commonly used and available at ATF.The ATF cooled CCD and Spiricon LBA500 image frame integrator will be synchronized to the beam and used to acquire and accumulate images of the angular distribution of the OTRI/ODR-OTRI with sufficient signal to noise, so that the interferences will be clearly visible above background. Image subtraction of the background will also be performed. This method has been commonly used by us in previous OTRI measurements [1].The charge per macropulse on ATF is equivalent to that of beams with which we have had previous experience and success in these types of measurements.

   We estimate approximately one or two hours of beam time per experimental run and two or three experimental runs will be sufficient to complete our proof of principle experiments.The position of the experimental cube will be placed such that the beam can be focused (x and y) to a waist condition at the site of the interferometer. A pair of quadrupoles and steering magnet will therefore be placed upstream of the diagnostics cube.We will work with the ATF staff and scientific users of the ATF beamlines to find a position which will minimally impact other experiments and which in fact may serve to provide useful data for their experiments. Our diagnostic foil system will be completely retractable to allow complete uninterrupted passage of the beam when it is not in use.

5 SUMMARY

We have shown in simulation codes, that the measurement of the divergence of a low energy low emittance electron beam can be made using ODR-OTR interferencesproduced by the unscattered portion of the beam passing through a perforated first foil of an ODR-OTR interferometer.With the proper proportion of holes to solid material and size of the perforations, interference fringes produced by ODR and OTR from unscattered electrons passing through the perforations of the first foil are clearly visible above the incoherent background light from the scattered portion of the beam. A proof of principle is necessary now to validate these Code predictions, which can readily be done at the ATF 30 MeV electron beam accelerator. This new technique could be very useful to measure low divergence, lower energy beams such as the 10 Mev MIRFEL accelerator being constructed at the University of Maryland, as well as higher energy, low emittance beams.

 

6 references

[1] R. B. Fiorito and D. W. Rule, “Optical Transition Radiation Beam Emittance Diagnostics”, in AIP Conference Proceedings No. 319, R. Shafer editor, (1994).

[2] M. L. Ter-Mikelian, High Energy Electromagnetic Processes in Condensed Media, Wiley-Interscience, New York, NY (1972).

[3] R. B. Fiorito and D. W. Rule, “Diffraction Radiation Diagnostics for Moderate to High Energy Charged Particle Beams”, Nuc. Instrum. and Meth. B, 173, 67-82 (2001).

[4] V. Verzilov, “Transition Radiation in the Pre-wave Zone”, Phys. Lett. A, 273, 135-140 (2000)