LONGITUDINAL PHASE SPACE MEASUREMENT FOR THE ADVANCEDSUPERCONDUCTING TEST ACCELERATOR PHOTOINJECTOR ∗

C.R. Prokop 1, P. Piot 1,2, M. Church 2, Y.-E Sun2

1 Department of Physics, Northern Illinois University DeKalb, IL 60115, USA2 Fermi National Accelerator Laboratory, Batavia, IL 60510, USA

AbstractThe Advanced Superconducting Test Accelerator

(ASTA) at Fermilab uses a high-brightness photoinjectorcapable of producing electron bunches with charges upto 3.2-nC, to be used in support of a variety of advancedaccelerator R&D experiments. The photoinjector in-corporates an extensive diagnostics suite including asingle-shot longitudinal phase-space diagnostics com-posed of a horizontally-deflecting cavity followed by avertical spectrometer. In this paper, we present the design,optimization, and performance analysis of the longitudinalphase space diagnostics.

INTRODUCTIONThe Advanced Superconducting Test Accelerator

(ASTA) [1, 2] currently under construction at Fermilabuses a high-brightness photoinjector capable of producingelectron bunches with charges up to several nCs. The∼ 40 MeV photoinjector [3] incorporates a chicane-basedmagnetic bunch compression (BC). In the first operatingphase, this BC will be the only one and will most probablybe operated to maximally compress the bunch resultingin peak currents in excess of 10 kA as predicted bysimulations [4]. Eventually this low-energy BC will bepart of the multi-stage compression scheme. To investigatethe performance of this low-energy BC, the installation ofa single-shot longitudinal-phase-space (LPS) diagnosticis planned. The LPS diagnostics are comprised of atransverse-deflecting cavity (TDC) followed by a verticalspectrometer. In this paper, we discuss the design, opti-mization, and anticipated performances of the diagnosticswith the help of single-particle-dynamics simulationscarried out with ELEGANT [5]. The capabilities and lim-itations of the diagnostics are also illustrated for realisticLPS distribution simulated with ASTRA [6].

BEAMLINE DESIGNThe single-shot LPS is comprised of a TDC operated at

zero-crossing that shears the beam in the horizontal plane,followed by a dipole magnet that energy disperses the beamin the vertical plane. The two processes combine to map

∗This work was supported by LANL Laboratory Directed Researchand Development (LDRD) program, project 20110067DR and by theU.S. Department of Energy under Contract No. DE-FG02-08ER41532with Northern Illinois University and under Contract No. DE-AC02-07CH11359 with the Fermi Research Alliance, LLC.

the longitudinal phase space (LPS) in to the (x, y) config-uration space that can then be directly measured using astandard density-monitor screen [7]. Therefore at the ob-servation location we have

x � Sxz0 + O(x0, x′

0) (1)

y � ηyδ0 + O(y0, y′

0) (2)

where (z0, δ0) are the coordinates in the LPS (δ is the rel-ative fractional momentum offset), and ηy and Sx are thedispersion and shearing factor computed at the screen lo-cation. The latter equation ignores remaining couplingas discussed below, and the subscript 0 indicates quanti-ties upstream of the TDC. In the thin-lens approximationSx = κL where L is the distance between the TDC andobservation screen and the normalized deflecting strengthis κ ≡ eVx

pc2πλwhere e, c, p, Vx and λ are respectively the

electronic charge, the speed of light, the beam momentum,the integrated deflecting voltage, and the wavelength of thedeflecting mode.

Figure 1: Overview of the LPS diagnostic section with as-sociated horizontal (blue) and vertical (red) betatron func-tion. The dispersion at X124 is ηy = 0.43 m.

Due to space constraints, the observation screen (X124in Fig. 1) is located at a distance L = 2.5m downstream ofthe TDC. One of the requirements is the ability to quicklydiagnose the beamwithout significantly disrupting the pho-toinjector magnetic lattice. Several options were consid-ered (including the optimization of the spectrometer dipoleentrance/exit face angle) and the most flexible solution thatcould accommodate the large variation in beam parametersarising from the wide range of operating charges (typicallyQ ∈ [0.02, 3.2] nC) was to use the quadrupole triplet lo-cated upstream of the TDC. The diagnostics beamline isdiagrammed in Fig. 1, beginning downstream of the exitof the low-energy bunch compressor. Given the incoming

Proceedings of IPAC2012, New Orleans, Louisiana, USA WEPPR034

05 Beam Dynamics and Electromagnetic Fields

D04 High Intensity in Linear Accelerators

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Courant-Snyder (C-S) parameters, the quadrupole triplet isset to minimize the betatron functions in both planes atX124’s location. The TDC is a 5-cell 3.9-GHz cavity [8]similar to the one used at the Fermilab’s A0 photoinjec-tor [9]. In its initial design it will be a Nitrogen-coolednormal-conducting cavity and will eventually be upgradedto a superconducting cavity.Several limiting factors prevent an exact mapping of the

LPS into the (x, y) space. First, as noted in Eq. 1 and2, contributions from the initial transverse emittances [theεx,0 inO(x0, x

′

0) and εy,0 inO(y0, y

′

0) terms] call for small

betatron functions at X124. Second, the TDC actually im-parts a correlation within the LPS due to its non-vanishingR65 ≡ 〈δ|z〉 [10]. Finally, a significant increase in energyspread can arise from the transverse dependence of the ax-ial electric field (Ez ∝ x) in the TDC. These limiting ef-fects impose conditions on the beam parameters that can becasted as

η2

yσ2

δ,0 βy εy,0 (3)

Sxσ2

z,0 βxεx,0 (4)

where the βs and σs are respectively the betatron func-tion at X124 and the initial root-mean square (rms) beamparameters and the εs are the geometric emittances. Forthe simulations presented in this paper, a strength of κ =2 m−1 is assumed as it corresponds to the maximumachievable value given the available rf power and past ex-perience. Given the simulated macroparticle distribution atX124, the coordinates of the macropaticles in the recon-structed LPS (zr, δr) are found from the transformation

zr =x

κL(5)

δr =y

ηy

− R65z (6)

To illustrate the effect of emittance, we use a grid-likeLPS, as shown in Fig. 2, which gives a clear example of theunderlying mechanism and complications that arise fromthe transverse emittance. In the case of an ideal zero-emittance beam, the LPS maps perfectly on to the x-yplane, with a “tilt” due to the non-vanishing R65 compo-nent, which can be corrected when scaling back down torecover the initial LPS.When a transverse emittance is added, it contributes to

the spot size, as demonstrated in Fig. 2. This effect in-creases the recovered bunch length and energy spread, andits uncorrelated nature with respect to z increases error inthe longitudinal emittance measurement.

TRANSVERSE COLLIMATIONIn addition to the emittance itself, transversely-

dependent energy gains from the TDC map the incomingx-x′ distribution to the y plane. Collimation can be usedto reduce these transverse contributions to the spot imagedat the screen. In Fig. 3, we us a realistic bunch distribution

Figure 2: The beam profile at the screen (top row) and re-constructed LPS distributions (bottom row) for transversenormalized emittances εx = εx = 0.0075 μm (left col-umn) and 0.75 μm (right column), showing the blurringeffect that results from the transverse distribution that in-creases with the emittance, the tilt that is a result of theR65 term of the TDC transfer matrix, and the reconstruc-tion process.

obtained fromASTRA simulations of the ASTA photoinjec-tor. For these simulations the charge per bunch is Q = 3.2nC and the bunch is compressed using a magnetic bunchcompressor. The observed LPS distortion arises from thequadratic correlation imposed by the rf wave form duringacceleration in the photoinjector; see Ref. [4]. The dis-tribution is tracked using ELEGANT throughout the LPS-diagnotics beamline. A screen with a 100 μm square holeplaced at the entrance of the TDC significantly improvesthe accuracy of the recovered image.As the aperture size increases, the reconstructed slice

energy spectrum smears out, resulting in an over-estimateof the rms fractional energy spread. This effect is illus-trated in Fig. 4 where energy histograms of macroparticlesin the center-most 180-μm longitudinal slice (the one withthe highest current) of the reconstructed LPS distributionare compared for different collimator sizes with the origi-nal LPS. For these simulation an idealized Gaussian bunchwith following paramters was considered: rms bunchlength σz=2.56 mm, rms slice energy spread σδe

=0.04%,energy chirp C=2 m−1, and a normalized transverse emit-tances of εx,y=5 μm.

RESOLUTION

In order to quantify the resolution of the proposedbeamline we consider a point-like initial LPS distributionΦ(z0, δ0) = Nδ(δ0)δ(z0) where the number of macropar-ticles N ∈ [2.5 × 104, 2.5 × 105], the upper limit beingused only for the case of a square collimator due to thelarge percentage of particles that are lost. The macropar-

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05 Beam Dynamics and Electromagnetic Fields

D04 High Intensity in Linear Accelerators

Figure 3: LPS distributions (top row) generated using AS-TRA after BC1 (left column), reconstructed from the screenwithout transverse collimation (middle column), and re-constructed with collimation using a 100-μm square aper-ture (right column), with each LPS’s current profile beneathit in the bottom row.

Figure 4: Area-normalized fractional-energy-spread his-tograms of macroparticles located in the center-most 180-μm longitudinal slice of the reconstructed LPS for achirped gaussian beam, for square collimators with sizesof 50 (blue), 140 (green), 387 (red), 1000 (cyan), and 3000(magenta) μm, and the pre-TDC LPS (yellow). The his-tograms are normalized to account for the number of parti-cles that are lost to the collimation.

ticles are distributed according to a Gaussian distributionin the transverse trace spaces with appropriate initial C-S

parameters (which match the ones displayed in Fig. 1) andvariable transverse emittances. The final rms sizes of therecovered LPS using the data simulated at X124 providesthe resolution of the LPS diagnostics. After proper cali-bration, the rms size in x and y respectively provide theresolution in energy and longitudinal coordinate (or time).In these studies we also investigate the effect of collima-tion using slits or apertures, of types similar to those pre-sented in the previous section. Figure 5 summarizes theinferred time (left plot) and energy (right plot) resolutionsfor the different configurations. As expected, collimatingthe initial distribution in the x direction can considerablyimprove the overall resolution and is especially beneficialin improving the energy resolution.

Figure 5: Longitudinal-coordinate (left) and fractional en-ergy spread (right) resolutions as a function of initial nor-malized emittances, εx=εy , for different collimation sce-narios (see legend).

REFERENCES[1] M. Church, et al, Proc. PAC2007, 2942 (2007).[2] J. Leibfritz, et. al, Proc. PAC2011, p. 118 (2011).[3] P. Piot, et al., Proc. IPAC2010, 4316 (2010).[4] C. Prokop, et al., Proc. IPAC2012, WEPPR033 (2012).[5] M. Borland, Advanced Photon Source LS-287, September

2000 (unpublished).[6] K. Flottmann, ASTRA: A space charge algo-

rithm, User’s Manual, (unpublished); available athttp://www.desy.de/∼mpyflo/AstraDokumentation

[7] A. H. Lumpkin, et. al, Proc. PAC2011, 510 (2011).[8] L. Bellantoni, Proc. LINAC06, 682 (2011).[9] T. W. Koeth, Proc. PAC07, 3665 (2007).[10] D. Edwards, ”Notes on Transit in Deflecting Mode Pillbox

Cavity”, unpublished (2007).

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D04 High Intensity in Linear Accelerators

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