L

Nonlinear Harmonics in the High-Gain Harmonic Generation(HGHG) Experiment

9S.G. Biedron, H. P. Freundt, S.V. Milton, L-.H. Yut+, and X.J. Wang++ *

fl “oQ*Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 G / ~

‘Science Applications International Corp., McLean, Virginia 22102 ~$~

‘tBrookhaven National Laboratory, Upton, New York 11973 A *S/’

L Introduction

A single-pass, high-gain free-electron laser (FEL) experiment based on the high-

gain harmonic generation (HGHG) theory is underway at the Accelerator Test Facility

(ATF) at Brookhaven National Laboratory (BNL) in collaboration with the Advanced

Photon Source (APS) at Argonne National Laboratory (ANL) [1]. This project achieved

first lasing in August 1999, when gain of 107 above spontaneous was measured [2,3]. It

has been shown through both the lD [4-7] and 3D [8] analytical models and in 3D

simulations [5-7] that the higher nonlinear harmonics are expected to grow at rates that

scale in inverse proportion to the harmonic number in all single-pass, high-gain FELs.

Also, the powers in these harmonics are expected to be substantial. An HGHG FEL

configuration already implements frequency up-conversion (as explained briefly in the

next section), and, in such a system, these higher nonlinear harmonics are unusually

interesting, as even shorter wavelengths can be exploited simultaneously. The specific

case of the simulated higher nonlinear harmonic output for the BNL/APS HGHG

experiment will be examined here.

II. High-Gain Harmonic Generation (HGHG) Theory

In a self-amplified spontaneous emission (SASE) FEL, the spontaneous emission

“noise” serves to ignite the FEL bunching process, resulting in a noisy output. In a seeded

The submitted manuscript hds been created by the University of Chicago as Operator of Argonne National Laboratory (“Argonne”) under Contract No. W-31-109-ENG-38with the U.S. Depwment of Energy. The U.S. Government retains for itself, and others acting on its behalf, a paid-up, nonexclusive, imevoeable worldwide liceme in s~dordcle to reproduce, prepare derivative works, distibute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

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(amplified) FEL, however, the output radiation quality is related to the coherence

properties of the seed. In both cases, the process saturates and maximum power is

reached. In practical design, this saturation point should be made to occur in the shortest

possible distance. It is well known that in order to achieve this, both SASE and amplifier

schemes require a high peak current, low emittance, and low energy-spread electron

beam, as well as a properly shimmed undulator, to reduce magnetic error effects on the

electron beam trajectory. From a machine user’s standpoint, the amplifier scheme is more

desirable due to the quality of the output radiation. To reach ultrashort wavelengths in

this mode of operation, however, a seed laser already at the desired short wavelength is

required. In the hard x-ray regime, for example, no seed is currently available.

Another possible mode of FEL operation capable of providing a very desirable

output light beam is HGHG [9,10]. Here, a coherent radiation source, at a subharmonic of

the desired output radiation wavelength overlaps an electron beam resonant with the seed

radiation. Energy modulation of the electron beam with a period equal to the seed

radiation is the result. Following this modulation, a dispersive section is traversed. Spatial

bunching is induced with a strong higher harmonic content. The beam then enters a

second undulator, the radiative section, tuned to resonance at the desired harmonic. (In

the BNL/A.PS HGHG experiment, the second harmonic is of interest.) Coherent radiation

and ultimately saturation at this higher harmonic is then achieved

number of undulator periods and with an excellent beam quality,

within a reasonable

as compared to the

SASE process. Recall that this better beam quality is defined by the coherent seed source.

Although this method has been proven at 5.3 ~m, it could quite possibly be extended to

higher energies, where the radiator is tuned to a much higher harmonic, and possibly

achieve

for the

saturation in the UV, VUV, or x-ray regimes. A schematic of the HGHG process

specific design case of the BNL/APS collaborative experiment is provided in

Figure 1.

111. Nonlinear Harmonic Generation in Single-Pass, Free-Electron Lasers

The nonlinear harmonics grow as bunching at the fundamental occurs. In a planar

undulator, which will be considered here, the natural motion of the electron beam causes

the odd harmonics to be most significant in the forward direction. It is important to

observe that all the harmonic growth rates are faster than the fundamental growth rate;

the gain length scales inversely with the harmonic number [4-8].

In order to illustrate this scaling, consider Maxwell’s equation in 1-D

where the electric field is given by

EX (z, t) = ~~ &h(z) exp[ihkO(z – et)] + cc. ,h

&NL)and the source current is given in terms of a nonlinear conductivity, ~ ,

(1)

(2)

(3)

$L) describes the linear interaction. The detailed form for the nonlinearwhere ~

conductivity is not specified here, yet it is included implicitly in the nonlinear

formulation. As stated above, these nonlinear terms are driven by bunching at the

fundamental, and so we can write Maxwell’s equations to lowest order as

(4)

Therefore, if the fundamental grows as & = exp~z ] then the harmonics will grow as

i: = exp[hrz], and the gain length scales as Lg = (2H’)-*. The scaling of the gain

length with the harmonic number is characteristic of the nonlinear mechanism. This is a

well-known phenomenon in traveling wave tubes (TWTS) [11], has been seen in a lD

analysis for the fust and third harmonics in an FEL [4-7], and was exemplified with a 3D

simulation code [5-7]. More recently, a 3D analytical model has been developed and

shows very good agreement with the previous work [8].

IV. Harmonic Output in the BNL/APS HGHG Case

The output power of HGHG at the fundamental, with respect to the resonance

condition of the radiative section of 5.3 pm, has been estimated [1,12]

have been made [2,3]. The theoretical calculations were performed

beam, seed laser, and magnetic parameters listed in Figure 1.

and measurements

using the electron

The HGHG simulations including the higher, nonlinear harmonics, relative to the

radiative section, were performed using the 3D, polychromatic, nonundulator averaged

code, MEDUSA

For a dispersive

MW (&=l.62 X

current of 110 A,

[13,14,5-7]. Again, the design parameters shown in Figure 1 were used.

strength of 1.7 kG (R56= 0.97 mm), an input seed laser power of 0.7

107V/m), an incoherent electron beam energy spread of 0.043%, a peak

, and a normalized ernittance of 4 n rnm-mrad, the powers as a function

of distance along the HGHG line are shown in Figure 2 for the fundamental of the

radiative section (5.3 ~) and its four higher harmonics. Note the radiative section begins

at 2.65 m. The higher harmonics are the second through fifth harmonics to the radiative

section resonant wavelength (5.3 ~m), but note they are the fourth, sixth, eighth, and

tenth harmonics of the input seed laser (10.6 pm). This multiplicative increase in the

Ifrequency up-conversion based on the ratio of the resonant wavelengths of the radiative

and modulative sections in HGHG makes these nonlinear harmonics even more fruitful

I than those found in SASE and amplifier schemes. In other words, in HGHG the shorter

I wavelengths are attainable more readily and with more control than the other schemes.

Note the above-described case has slightly better performance than the nominal

beam case for the fimdamental as well as the harmonics and was found by lowering the

dispersive section from 2.30 kG to 1.7 kG (reducing RS6from 1.67 mm to 0.97 mm). In

I addition to the simulations at this case, parameter scans were performed by varying

I dispersion section strength, seed laser power density, emittance, energy spread, and peak

I current, about the nominal design case. Figures 3-7 show the output power and saturation

I length for each of these scans for the fundamental of the radiative section (5.3 pm) and

the four higher harmonics (2.65, 1.77, 1.33, and 1.06 Lm).

I Upon examination of the parameter scans of dispersive section strength and the

Iinput seed power, some comments can be made. Both of these parameters contribute to

the efficiency of the HGHG process and the results of the scans resemble each other

greatly. For example, reduced HGHG efficiency will result from too little energy

I modulation or, alternatively, too little phase-space rotation in the dispersive section leads

Ito an underbunched electron beam at the entrance of the radiative section. Reduced

HGHG efficiency will also result from too much energy modulation or too much phase-

space rotation in the dispersive section as the beam is overbunched when entering the

radiative section. Basically, there is a balance between saturated output power and

saturation length based on the dispersive section strength and the degree of energy

modulation. The optimum HGHG efficiency, if based solely on the degree of energy

modulation and dispersive strengths, is the shortest distance to saturation in the radiative

section. The equation governing this optimum is expressed as

3DisptmiveStwion=/~ .-

Ma.ximumhserlnducedkfodulution

The saturated power decreases fairly readily with degraded electron beam energy

spread, peak current, and emittance, and increases with beam quality. The saturation

length also increases with electron beam degradation and is reduced as the beam quality

sharpens.

v. Conclusion

The nonlinear harmonic output in all single-pass, high-gain FELs is important, as

shorter wavelengths are achievable. The harmonic output from HGHG is particularly

interesting, however, since even shorter wavelengths can be achieved in such a

configuration, and they are imprinted for coherence unlike the noisy SASE case. (The

same is true when using the Bonofacio et al. two-undulator scheme [15] as well.) In this

presentation, the harmonic output from HGHG was shown in simulation by sensitivity

studies of

BNL/APS

the fundamental and four higher harmonics

HGHG experiment. Harmonic measurements

of the radiative section of the

are ongoing at this experiment

and have proven to be comparable to theory/simulation [16].

This harmonic experiment will also be performed for the fundamental and second

harmonic with wavelengths of 530 and 265 nm, respectively, corresponding to an

electron beam energy of=217 MeV in a purely SASE mode of operation at the Advanced

Photon Source’s SASE FEL at Argonne National Laboratory [7,17].

It is the desire of the light source community to achieve shorter wavelengths, on

the order of 1 & and various prototypical experiments other than HGHG are underway

[18] using the fundamental radiation. To achieve even shorter wavelengths with lower

electron beam energies, the nonlinear harmonics, which are generated in self-amplified

spontaneous emission (SASE), amplifier, and HGHG FEL schemes, will be important. In

addition, the use of soft x-ray seed lasers [19] along with combinations of the above

schemes will also be important in obtaining these shorter wavelengths [20-21].

VI. Acknowledgements

Many thanks our extended to our HGHG collaboration friends Marcus Babzien,

Adnan Doyuran, and Timur Shaftan for helping with the experimental measurements.

This work is supported by the U.S. Department of Energy, Office of Basic Energy

Sciences, under Control No. W-3 1-109-ENG-38.

VII. References

[1] L.-H. Yu, M. Babzien, I. Ben-Zvi, L.F. DiMauro, A. Doyuran, W. Graves, E.

Johnson, S. Krinsky, R. Malone, I. Pogorelsky, J. Skaritka, G. Rakowsky, L. Solomon,

X.J. Wang, M. Woodle, V. Yakimenko (BNL), S.G. Biedron, J.N. Galayda, V. Sajaev, I.

Vasserman (ANL), “The Status of a High-Gain Harmonic Generation Experiment at the

Accelerator Test Facility,” Proceedings of the IEEE 1999 Particle Accelerator

Conference, (1999) 2470.

[2] L.-H. Yu, M. Babzien, I. Ben-Zvi, L.F. DiMauro, A. Doyuran, W. Graves, E.

Johnson, S. Krinsky, R. Malone, 1. Pogorelsky, J. Skaritka, G. Rakowsky, L. Solomon,

X.J. Wang, M. Woodle, V. Yakimenko (BNL), S.G. Biedron, J.N. Galayda, E. Gluskin, J.

Jagger, V. Sajaev, I. Vasserman (ANL), “First Lasing of a High-Gain Harmonic

Generation Free-Electron Laser Experiment,” Nucl. Instrum. Meth. A445 (2000) 301

[3] L.-H. Yu, M. Babzien, I. Ben-Zvi, L.F. DiMauro, A. Doyuran, W. Graves, E.

Johnson, S. Krinsky, R. Malone, I. Pogorelsky, J. Skaritka, G. Rakowsky, L. Solomon,

X.J. Wang, M. Woodle, V. Yakimenko (BNL), S.G. Biedron, J.N. Galayda, E. Gluskin, J.

Jagger, V. Sajaev, I. Vasserman (ANL), “High-Gain Harmonic Generation Free-Electron

Laser:’ accepted to Science, in press.

[4] R. Bonifacio, L. DeSalvo, and P. Pierini, “Large Harmonic Bunching in a High-Gain

Free-Electron Laser,” Nucl. Instrum. Meth. A293 (1990) 627.

[5] H.P. Freund, S.G. Biedron, S.V. Milton, “Nonlinear Harmonic Generation in Free-

Electron Lasers,” IEEE Journal of Quantum Electronics 36 (2000) 275.

[6] S.G. Biedron, H.P. Freund, and S.V. Milton, ‘(3D FEL code for the simulation of a

high-gain harmonic generation experiment,” in Free-Electron Laser Challenges II,

Harold E. Bennett, David H. Dowell, Editors, Proceedings of SPIE 3614 (1999) 96.

[7] H.P. Freund, S.G. Biedron, S.V. Milton, “Nonlinear Harmonic Generation and

Proposed Experimental Verification in SASE FELs,” Nucl. Instrum. Meth. A445 (2000)

53.

[8] Z. Huang and K. Kim, “Nonlinear Harmonic Generation of Coherent Amplification

and Self-Amplified Spontaneous Emission,” Proceedings of the 22nd Annual Free-

Electron Laser Conference, Durham, North Carolina, August 13-18,2000.

[9] L.-H. Yu, “Generation of intense uv radiation by subharrnonically seeded single-pass

free-electron lasers,” Phys. Rev. A44 (1991) 5178.

[10] 1. Ben-Zvi et al., “Design of a harmonic generation free-electron laser experiment at

Brookhaven National Laboratory,” Nucl. Instrum. Meth. A318 (1992) 208.

[11] J.W. Hansen, G.A. Lange, A.S. Rostad and R.L. Woods, “System aspects of

communications TWTAs on how to deal with the tube manufacturer to your best

advantage,” Hughes Aircraft Company Electron Dynamics Division Applications Note,

August 1992.

[12] HGHG Design Handbook, BNL Report (1996).

[13] H.P. Freund, “Nonlinear theory of short wavelength free-electron lasers,” Phys. Rev.

E52 (1995) 5401.

[14] S.G. Biedron, H.P. Freund, L.-H.Yu, “Parameter Analysis for a High-Gain

Harmonic Generation FEL Using a Recently Developed 3D Polychromatic Code:’ Nucl.

Instrum. Meth. A445 (2000) 95.

[15] R. Bonifacio, L. de Salvo Souza, P. Pierini, and E.T. Scharlemann, “Generation of

XUV light by resonant frequency tripling in a two-wiggler free-electron laser amplifier,”

Nucl. Instrum. Meth. A296 (1990) 787.

[16] A. Doyuran, L.-H. Yu, M. Babzien, I. Ben-Zvi, L.F. DiMauro, W. Graves, E.

Johnson, S. Krinsky, R. Malone, I. Pogorelsky, J. Skaritka, G. Rakowsky, T. Shaftan, L.

Solomon, X.J. Wang, M. Woodle, V. Yakimenko (BNL), S.G. Biedron, J.N. Galayda, E.

Gluskin, J. Jagger, V. Sajaev, I. Vasserman (ANL), “High Gain Harmonic Generation

Experiment,” Proceedings of the 22ndAnnual Free-Electron Laser Conference, Durham,

North Carolina, August 13-18,2000.

[17] S.V. Milton, E. Gluskin, S.G. Biedron, R.J. Dejus, P.K. Den Hartog, J.N. Galayda,

K.-J. Kim, J.W. Lewellen, E.R. Moog, V. Sajaev, N.S. Sereno, G. Travish, N.A.

Vinokurov et al., “Observation of Self-Amplified Spontaneous Emission and Exponential

Growth at 530 rim,” Phys. Rev. Lett. 85 (.2000)988.

[18] S.V. Milton et al., “FEL Development at the APS: The APS SASE FEL,” in Free-

Electron Laser Challenges H, Harold E. Bennett, David H. Dowell, Editors, Proceedings

of SPIE 3614 (1999) 86; The VISA Collaboration (BNL, LANL, LLNL, SLAC, UCLA),

VISA Proposal, “Proposal for a SASE-Free-electron Laser Experiment, VISA, at the

ATF Linac,” April 1998; “A VUV Free Electron Laser at the TESLA Test Facility at

DESY: Conceptual Design Report,” DESY Print, TESLA-FEL 95-03, June 1995; LCLS

Design Study Group, Linac Coherent Light Source (LCLS) Design Study Report, SLAC-

R-521 (1998).

[19] S.G. Biedron, H.P. Freund, S.V. Milton, Y. Li, “Simulation of the fundamental and

nonlinear harmonic output from an FEL amplifier with a soft x-ray seed laser,”

Proceedings of 7* European Accelerator Conference (EPAC) 2000, 26-30 June, Vienna,

to be published.●

[20] S.G. Biedron, S.V. Milton, and H.P. Freund, “Modular Approach to Achieving the

Next Generation Light Source,” Proceedings of the 22nd Annual Free-Electron Laser

Conference, Durham, North Carolina, August 13-18,2000.

[21] L.H. Yu and J. Wu, “Cascading Stages of High-Gain Harmonic Generation to

Produce Coherent Hard X-rays,” Proceedings of the 22nd Annual Free-Electron Laser

Conference, Durham, North Carolina, August 13-18,2000.

List of Figures:

Figure 1: The BNL/APS HGHG experimental layout.

Figure 2: Power (W) versus distance (m) along the HGHG line for the (a) 5.3 pm, (b)

2.65 pm, (c) 1.77 ~m, (d) 1.33 pm, and (e) 1.06pm output radiation.

Figure 3: Saturation Length (m) and Saturated Power (W) versus dispersive section

strength (kG) for the (a) 5.3 pm, (b) 2.65 pm, (c) 1.77 pm, (d) 1.33 pm, and (e) 1.06 ~

output radiation.

Figure 4: Saturation Length (m) and Saturated Power (W) versus input seed laser power

(MW) for the (a) 5.3 pm, (b) 2.65 ~, (c) 1.77 pm, (d) 1.33 pm, and (e) 1.06pm output

radiation.

Figure 5: Saturation Length (m) and Saturated Power (W) versus energy spread (%) for

the (a) 5.3 pm, (b) 2.65 pm, (c) 1.77 pm, (d) 1.33 ~, and (e) 1.06pm output radiation.

Figure 6: Saturation Length (m) and Saturated Power (W) versus peak current (A) for the

(a) 5.3 ~m, (b) 2.65 pm, (c) 1.77 pm, (d) 1.33 pm, and (e) 1.06pm output radiation.

Figure 7: Saturation Length (m) and Saturated Power (W) versus emittance (n mm-mrad)

for the (a) 5.3 pm, (b) 2.65 ~m, (c) 1.77 pm, (d) 1.33 #m, and (e) 1.06 pm output

radiation.

ModulativeSection RadiativeSection:Seed~ase~ BW=0.16T BW=0.47T HGHGF.lX:L= 10.6w ~W=8cm ~W=3.3cm X.5.3UHIP* =0.7Mw L=0.76m P* =3SMW

/

Dupersive Section:&#t(Jy=22

L=03m \ElectronBeamInputiE=40MeV

ElectronBeamOut&m=4x mm-mrad@’y=0.043%~k= 110Aze=4ps

Figure 1: The BNIJAPS HGHG experimental layout

3.0

?..s

S.O

0.0

10’

10’ -10’

io’

10’

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I 1 I t

-

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3.010’

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0.010”

01 2 34 56

z (m)

(a)

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z (m)

3.0

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5,0

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10’

10’

10’

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10’

10’

10”

(b)

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(c)

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80,0] :~

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‘c

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fin I I t 1. .

z (m)

(d)

Figure 2: Power (W) versus

0 0.8 1.6 2.4 3.2 4 4.8 3.6

z (m)

(e)

distance (m) along the HGHG line for the (a) 5.3 pm,

(b) 2.65 pm, (c) 1.77 ym, (d) 1.33 pm, and (e) 1.06pm output radiation.

_ 5.3 mixon Sat. LOnglhIt

- ‘*. - S.3 micron Sat PowerI

—9-2.6s mkxan Sat. Length 1[ . ‘-- -2.65 mlcmn sat Powe,

66k“’’’’’’’’”’’’’’’”

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(a)

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Dispersive Section Sssength

(c) (d)

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0 0.5 1 13 2 2.5 3 3.5

-- 5.3

5.?

Dispersive Section Strength

(e)

Figure 3: Saturation Length (m) and Saturated Power (W) versus dispersive section

strength (liG) for the (a) 5.3 pm, (b) 2.65 ~m, (c) 1.77 ~m, (d) 1.33 pm, and (e) 1.06

~m output radiation.

~ S.3 nrlcrofl Sal. Length II --● .-5.3micron Sat- Power I7 .s 2.5 10’i 1 i 1

.s.

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(a)

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Seed Laser Power

(e)

Figure 4: Saturation Length (m) and Saturated Power (W) versus input seed laser

power (MW) for the (a) 5.3 pm, (b) 2.65 pm, (c) 1.77 pm, (d) 1.33 ~m, and (e) 1.06

pm output radiation.

10’

w10’ :

210’

10’

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Energy Spread

(e)

Figure 5: Saturation Length (m) and Saturated Power (W) versus energy spread(%) for the (a) 5.3 pm, (b) 2.65 Vm, (c) 1.77 ~m, (d) 1.33 pm, and (e) 1.06 ym output

radiation.

~ 2.SS mkfon Sat. Langlh{I -- ● - ‘2.S5 micronSat. Poww

I_ S.3 mkxon Sat. Length

J-. ● . .5.3 micron Sat Power

I

S8 }’”’’’’’’’’’’’’’’’’’.’ ”’”4 t 10’ S.2

,, ~ ,50 100 1so 200 250 300

Peak Current

Fl!ll”? *,.,...l.i.i..-.4”42 0

so 100 1so 200 2 so 300

Peak Current

(a)

_ 1.77 mcron Sat. Langth 11 --s.-1.77 micron SaL PowarI

_ 1.33 mkron Sat. LengthII

--~-- l.33 micron Sat Power1

5.6 3.5 [045.0 E“”’’’’ ’’’’’’’’’’’’’’’hi*6 10’

I,kl●......q.-

49 . 5 10’

.-4.3 4 10’

4.7 3 10’

4,6 1 10’.“

4.3 . 1 10’

4.4 050 100 I 50 200 2s0 300

. . 0. .50 100 150 200 250 300

Peak CurrentPeak Current

(c) (d)

_ 1.06 mixon Sat. LengthII

-- 3-- l.oe micron Sat Power I

X..-

d

. . . .

-50 100 f 50 200 250 300

Peak Current

(e)

Figure 6: Saturation Length (m) and Saturated Power (W) versus peak current (A)

1.77 pm, (d)l.33 pm,and(e)l.06 prnoutput

radiation.

for the (a) 5.3 ym, (b) 2.65 pm, (c)

_ S.3 micron Sat. L eng;hII

. . ● .5.3 micron Sat POweI I$.2

151O’Uw

,, ~ , ,;012345 678

Emittance

(a)

_ 1.77 micron Sat. LengthII

- . ● - - 1.77 micron Sat. PowerI

S.1

~,,~0 I 234 367 8

Emittance

6 10’

s 10’ .:

4

34 [0’ -.~

3 10’ g

&210’ ~

=5

1 10’ 2

0

(c)

_ 1.06 micron Sat. Length I

3,1

_ 2.85 mcron Sat. Length 11 -- ● . ‘2.85 micron Sat power1

& 1.8

1.. .0 I 234567 8

Emittance

s 10’

0

_ 1.33 micron Sat. Leng!hII

-- ● - -1.33 micron SaL PowerI

“~ 3000

(d)

-- ● .- 1.06 micron SaL PowerI

4.s t,,,, L.acl,,,:. t,!.,,, !.,,,,, f,. <O

01 234 67 8

Emittanc~

(e)

10’

.

Figure 7: Saturation Length (m) and Saturated Power (W) versus emittance (Z mm-

mrad) for the (a) 5.3 pm, (b) 2.65 ym, (c) 1.77 pm, (d) 1.33 ~m, and (e) 1.06 pm

output radiation.