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Nuclear Instruments and Methods in Physics Research A .“” “““r’ “’ -’

ELSEVIER

Performance simulation and parametershort wavelength FEL

G. Travish *

NUCLEAR

INSTRUMENTS

8 METHODS

IN PHYSICS

RESEARCHs e c m n

optimization for high gainamplifiers

UCLA Departtnent of Physics, Los Angeles, CA 90024, USA

AbstractThe designers of short wavelength FELs must rely on theoretical and numerical predictions since no experimental data

are available for this region. The numerical codes which have been developed, and are being used to design systems atSLAC, BNL, Duke, LBL, CEBAF, LANL and UCLA among others, contain our best theoretical understanding of thesesystems. This paper analyses the present simulation capabilities for short wavelength designs. We discuss how codes areused to design these new systems, which aspects of our models are well implemented and which are not, methods ofverifying the models, comparison with experiment, and finally comments on extrapolating to short wavelengths.

1. Overview

Recently, a number of FEL proposals have been putforth in an attempt to provide users with high brillianceradiation at short wavelength (UV and beyond) [l-3].These new systems propose to operate in wavelength andgain regimes far away from past or present FELs (see Fig.1). While these new designs offer great promise by using

state of the art beam and undulator quality, the perfor-mance claims must be carefully examined. Computer simu-lation being the most powerful tool used to predict theperformance of new FELs leads one to investigate ourpresent simulation capabilities.

We discuss in this paper the present computation capa-bilities for high gain, short wavelength FEL amplifiers.High gain implies many exponential gain lengths of growthof spontaneous emission or an injected signal, while shortwavelength is used to indicate “wavelengths shorter thanpresently achieved” - deep UV and beyond. FEL perfor-mance can be modeled with various scaled parameters[4-61; however, to determine the predictability of simula-tions we use wavelength as a fundamental parameter.

2. How FEL codes are presently u s e d

The complexity and cost (in CPU time) associated withrunning three dimensional FEL codes along with the largeparameter space available to explore, requires the use of

_ Corresponding author. Tel. 1 310 206 5584. fax + 1 310

206 1091, e-mail [email protected].

simpler and quicker means for initial design work. Oftenone begins with one dimensional analytic formulas inorder to chose an operating regime. More elaborate modelswhich include diffraction, energy spread, etc. and areeasily implemented in spread sheets or mathematics solverscan then be used to perform an initial exploration of adesign’s sensitivity to parameters (an example is given inFig. 2) [7]. A promising design can then be studied using

three dimensional or multifrequency numerical codes.An interesting question is whether the above process

would be necessary if sufficient computing power wereavailable. An incomplete answer is yes, since changes tothe model (code) would still be more easily implementedin the analytic or spread sheet calculations. At present. it istime and CPU intensive to perform an exhaustive set offully three dimensional, multifrequency simulations of agiven design. As an example, for a given version of theSLAC LCLS, hours of NERSC Cray C-90 CPU time arerequired to perform three dimensional sensitivity studies.

A more relevant question is whether it is the numericalmodels or the measurement accuracy of beam and undula-tor parameters that limit present FEL performance pre-dictability. With virtually no experimental data in the highgain short wavelength regime, this question will go unan-swered here, save for a few comments in subsequentsections.

3. Strengths and weaknesses of the models

The question of what features of an FEL are modeledwell by simulations would perhaps be answered differently

by experimentalists and theorists: one experimentalist’s

016%9002/9.5/$09.50 0 1995 Elsevier Science B.V. All rights reservedSSDl 0168-9002(94)01413-2

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G. Tracish / Nucl. Instr. and Meth. in Phys. Rex A 358 (1995) 48-51 49

10’ 100 lo” 1o.a lo” IO”Wavelength wm]

Fig. 1. Gain versus wavelength for a number of past FELs is plotted on a log-log scale. The shaded area represents the regime of thevarious recently proposed high gain, short wavelength FELs.

answer will be given here. The statements below hold ingeneral for available codes; some comments may not applyto a particular code or set of parameters.

Let us begin with the good news. Simulations caninclude virtually any theoretically predicted or experimen-tally measured effect. New phenomena such as optical

guiding was first “observed” through the use of numericalcodes [s]. Parameters which are experimentally robust oraccurately measurable have reliable numerical models.Simulations of high gain amplifiers can include startupfrom noise, optical guiding, slippage, harmonic generation,

Fig. 2. An example of a multivariable optimization using a threedimensional semi-analytic model [26]. The parameters used hereare similar to recent LCLS studies. The saturation length is plottedas a surface of the focusing beta function of the undulator period(assuming a fixed wavelength).

multi-undulator systems, and undulator and alignment er-rors. However, in order to reduce the complexity and runtime of the programs, different codes have been written toincorporate some, but not all of these effects (see Table 1).

Beam current and energy spread are considered wellmeasured experimentally, and hence are well modeled

numerically. Some codes can implement current distribu-tions directly from field solvers or experimental data [9].Another parameter which is in hand is beam steering errorsdue to mismatch and undulator field errors that are wellmodeled in three dimensional codes. Furthermore, straightforward BPM and steering magnet corrector schemes areimplemented and understood both experimentally andwithin codes. The saturation regime also is well modeledin numerical codes, while useful analytic theories are stilllacking [IO]. A significant issue for short wavelength FELswhich has received little experimental attention, but ap-pears to be well modeled, is external focusing throughquadrupoles, sextupoles, plasmas or other means [111.Complex simulations including multiple undulators anddispersion sections are also implemented in some codes[ 1 2 1 .

The “less good” news is that there are a number ofeffects which may not be well modeled, but withoutexperimental verification it is difficult to emphaticallystate if our models are accurate. Emittance is both difficultto measure and model, as mathematical models for, e.g.,rms emittance do not contain information about distribu-tion function correlations. As a result, few analytic modelsmake claims about slice emittance versus cooperationlength emittance or beam core emittance versus the emit-

tance within an optical mode. The lack of theoreticalguidance makes a study of emittance effects incomplete

II. SINGLE PASS UV/X-RAY FELs

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50

Table 1A sample of FEL codes and some of their features [19-241. Some codes have features not listed, others have limited capability in unmarkedcategories. For example, most codes have external focusing implements. but only ones with discrete focusing channels (not smoothapproximations) were indicated.

Code name

lD/2D/3DTime dependentMultiundulatorDispersion sectionStartup modelSteering errorsUndulator errorsFocusingHarmonicsOptical modes

FELEX

3

yesyes

yesyesyes

yesyesyes

FRED3D

3

yes

yesyesyes

Yes

GINGER

2

yesyes

yes

NUTMEG

2

YCSyes

yes

SARAH

1

yes

yes

TDA3D

3

yes

yes

yes

yes

and time consuming. Multifrequency codes can modelvarious emittance distributions, but only with azimuthalsymmetry or with extensive run times. Issues such asfluctuations, startup from noise and superradiance are alsonor well tested nor sufficiently sophisticated [13]. As anexample, startup from noise is often simulated by assum-ing an input signal equal to the spontaneous emissionwithin one power gain length. Multifrequency codes alsogenerate particle distributions with the correct Poissonstatistics to emulate spontaneous emission levels whichagree with analytic models. However, neither of thesemodels may be sufficient to account for experimentalconditions where a beam distribution may not be com-pletely uncorrelated. As is discussed in Section 5, startuplevels have yet to be well modeled.

The disparity between the - lo4 particles used insimulations and the - 10” particles in a beam maypresent a formidable problem. At issue is the number ofparticles, Nh, within a cubic (resonant) wavelength. Forparticle distributions with Nh > 1 higher spontaneous emis-sion levels are expected due to coherent emission. Codescan model such distributions by simulating only a slice ofthe beam, and hence reduce the effective beam volume.

Whether such approximations underestimate the actualstartup level, or even contain the appropriate effects, isunclear without experimental measurements of SASE.

4. Model verification

Assuring the validity of a simulation requires bothprogramming skills and physical insight. Codes often dif-fer in the numerical methods used to solve a model and inthe assumptions made in the model [14]. Agreement be-tween two codes often lends credence to both programs:discrepancies often lead to improvements. Simulation re-sults can also be checked against simplified models. Usingparameter sets within one dimensional limits (no energy

spread, smooth focusing, no diffraction or other assump-tions) allows rapid comparison with analytic results. Addi-tionally, numerical diagnostics (phase space plots, energyconservation checks, bunching parameters, etc.) can begenerated within a program allowing for further verifica-tion of model performance. Nevertheless, numerical com-parisons and verifications do not substitute for experimen-tal authentication.

5. Comparison with experiment

A pessimist’s version of this section would be veryshort: there are no short wavelength. high gain experi-

Table 2Comparison of the predicted and experimentally measured effective startup power for some of microwave FELs [25].

FEL name h,(f) 1, px102 F Predicted Measured(kA) noise (mW) noise (mW)

ELF 8 mm (35 GHz) 1 5.0 1.0 0.4 1.5ELF 3 mm (94 GHz) 1 3.5 1.4 0.5 30ELF 2 mm (140 GHz) 1 2.8 2.5 0.4 175

PALADIN 10.6 (30 THz)m 1 0.8 1.5 40 ?IMP 1.2 mm (250 Ghz) 3 4.0 0.8 5.3 ?

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