- Email: [email protected]
Optical power evolution in the Boeing 1 kW FEL oscillator
a_. .__
Nuclear Instruments and Methods in Physics Research A 375 ( 1996) 358-359
__ ll!B
NUCLEAR INSTRUMENTS 8 METHODS IN PHYSICS RESEARCH
SectronA
ELSEVIER
Optical power evolution in the Boeing 1 kW FEL oscillator J. Blau, R.K. Wong, W.B. Colson* Physics Depurtment,
Naval Postgraduate
School. Monterey,
CA, USA
Abstract A four-dimensional simulation in x. y, z, and t, including betatron motion of the electrons, evolution and the trapped-particle instability in the Boeing 1 kW EEL oscillator.
Boeing is designing a visible, high power free electron laser (FEL) oscillator, to produce 1 kW average power at a wavelength A = 0.63 pm [I]. The large electron beam current of Z-500 A will pass through an L = 5 m long, N = 220 period undulator, creating strong optical fields inside a resonator cavity. Simulations show this may lead to sideband growth and the onset of the trapped-particle instability. Increasing the outcoupling and tapering the undulator would lessen these effects. Fig. 1 shows the results from a multi-mode four-dimensional simulation in (x, y, z, t) of the Boeing oscillator, for n = 50 passes. The longitudinal coordinate z is scaled to the slippage length NA, and the transverse coordinates (x, y) are scaled to the characteristic optical mode radius (LA/n)“‘. The model includes the betatron motion of the
ID
1
Nvolution
Wrap
0e30.5
LSo=l
a,=11
cTp.4
&l-l
0”-6.4
N.220
6-O
z-=0.5
Q=20
e=0.01
P
la(z.n)I
0
FEL
j-1600
”
0
996
n
50
-201
1
la(xrn)
P(V#sl)
”
201
0
n
1
50
Fig. 1. Multi-pass evolution of the Boeing 1kW FEL oscillator, Q = 20. * Corresponding author. Tel. + 1408 656 2896, fax + 1 408 656 2834. e-mail [email protected].
is used to study optical power
electrons, and follows their evolution in phase space using the FEL pendulum equation [2]. The optical wavefront evolves via the parabolic wave equation. Since the pulse length (7 ps) is long compared to the slippage distance, only one slippage length of the electron and optical pulses is followed in the simulation, with periodic boundary conditions assumed at z = 20.5. With a dimensionless current density j = 1800. and high cavity Q = 20, large optical fields develop rapidly inside the oscillator, creating deep potential wells in phase space. The bunched electrons undergo synchrotron oscillations, leading to sideband formation, as shown in the evolution of the optical spectrum, P( v, n) in the center of Fig. I. The sidebands are amplified each pass, modulating the held envelope la(z, n)l shown on the left. Thus. the trappedparticle instability [3] produces a broad, chaotic spectrum. The final spectral width is Ah/A= Au/2~rN = 5%. The average output power is 65 W. after accounting for the overall system duty factor. To achieve more output power, it is necessary to increase the outcoupling. This could also reduce the fields inside the cavity enough to prevent sideband growth. Fig. 2 shows the results of a simulation with Q = 5. The power inside the cavity is about the same as the previous simulation, but with the increased outcoupling, it corresponds to an increased output power of 250 W. Since there is still so much power stored inside the cavity, sidebands are still present in the optical spectrum. However, the spectral width is reduced slightly to AA/A = 3.5%. Another way to prevent the trapped particle instability is to taper the undulator. This should cause about half of the electrons to become untrapped, which would reduce the synchrotron oscillations. In Fig. 3, the undulator is given a 10% taper in resonant energy S = -4-n Ayly = 88 n. The average output power is increased to 43 W, but the power evolution P(n) shows significant oscillations. This may be due to sporadic attempts at sideband formation. The sideband growth is reduced significantly, and the spectral
0168.9002/96/$15,00 Copyright 0 1996 Elsevier Science B.V. All rights reserved SSDI 0168.9002(95)01187-O
J. Blnu et al.
4n
mn
I Nucl. Instr.
and Mrth.
o_=os
no=1
0&l
Og'l.4
68.1
0 =8.4 P
Nl220
a=0
no=o.5
Q=5
e-o.01
1080
0
358-359
359
rwolution
Wrap
j-1800
la(z.n)I
in Phvs. Res. A 375 (1996)
Pw,n)
la(x.n)
I
50
50
0
n
Fig. 2. Multi-pass
50 -201
evolution
v
2010
of the Boeing
n
50
1kW FEL oscillator.
0
n
50 -20.1
Fig. 3. The Boeing oscillator
"
2010
11
with a tapered undulator.
50
6 = 88-a.
Q =5.
width is now only AMA = 1%. Increasing the outcoupling or the system duty factor would be necessary to achieve I kW average power.
The authors
[Jl J. Adamski et al., white paper Space Group.
(1994)
Boeing
Defense
&
[21 W.B. Colson. in: Free Electron Laser Handbook, eds. W.B. Colson, C. Pellegrini and A. Renieri (Elsevier. Amsterdam, 1990) chap. 5.
Acknowledgements for support of this work by the School, and SURAICEBAF.
are grateful
Naval Postgraduate
References
[31 N.M. Kroll and M.N. Rosenbluth, Electronics, vol. 7 (1980) 147.
Physics
of Quantum
VI. HIGH POWER
FELs
Nuclear Instruments and Methods in Physics Research A 375 ( 1996) 358-359
__ ll!B
NUCLEAR INSTRUMENTS 8 METHODS IN PHYSICS RESEARCH
SectronA
ELSEVIER
Optical power evolution in the Boeing 1 kW FEL oscillator J. Blau, R.K. Wong, W.B. Colson* Physics Depurtment,
Naval Postgraduate
School. Monterey,
CA, USA
Abstract A four-dimensional simulation in x. y, z, and t, including betatron motion of the electrons, evolution and the trapped-particle instability in the Boeing 1 kW EEL oscillator.
Boeing is designing a visible, high power free electron laser (FEL) oscillator, to produce 1 kW average power at a wavelength A = 0.63 pm [I]. The large electron beam current of Z-500 A will pass through an L = 5 m long, N = 220 period undulator, creating strong optical fields inside a resonator cavity. Simulations show this may lead to sideband growth and the onset of the trapped-particle instability. Increasing the outcoupling and tapering the undulator would lessen these effects. Fig. 1 shows the results from a multi-mode four-dimensional simulation in (x, y, z, t) of the Boeing oscillator, for n = 50 passes. The longitudinal coordinate z is scaled to the slippage length NA, and the transverse coordinates (x, y) are scaled to the characteristic optical mode radius (LA/n)“‘. The model includes the betatron motion of the
ID
1
Nvolution
Wrap
0e30.5
LSo=l
a,=11
cTp.4
&l-l
0”-6.4
N.220
6-O
z-=0.5
Q=20
e=0.01
P
la(z.n)I
0
FEL
j-1600
”
0
996
n
50
-201
1
la(xrn)
P(V#sl)
”
201
0
n
1
50
Fig. 1. Multi-pass evolution of the Boeing 1kW FEL oscillator, Q = 20. * Corresponding author. Tel. + 1408 656 2896, fax + 1 408 656 2834. e-mail [email protected].
is used to study optical power
electrons, and follows their evolution in phase space using the FEL pendulum equation [2]. The optical wavefront evolves via the parabolic wave equation. Since the pulse length (7 ps) is long compared to the slippage distance, only one slippage length of the electron and optical pulses is followed in the simulation, with periodic boundary conditions assumed at z = 20.5. With a dimensionless current density j = 1800. and high cavity Q = 20, large optical fields develop rapidly inside the oscillator, creating deep potential wells in phase space. The bunched electrons undergo synchrotron oscillations, leading to sideband formation, as shown in the evolution of the optical spectrum, P( v, n) in the center of Fig. I. The sidebands are amplified each pass, modulating the held envelope la(z, n)l shown on the left. Thus. the trappedparticle instability [3] produces a broad, chaotic spectrum. The final spectral width is Ah/A= Au/2~rN = 5%. The average output power is 65 W. after accounting for the overall system duty factor. To achieve more output power, it is necessary to increase the outcoupling. This could also reduce the fields inside the cavity enough to prevent sideband growth. Fig. 2 shows the results of a simulation with Q = 5. The power inside the cavity is about the same as the previous simulation, but with the increased outcoupling, it corresponds to an increased output power of 250 W. Since there is still so much power stored inside the cavity, sidebands are still present in the optical spectrum. However, the spectral width is reduced slightly to AA/A = 3.5%. Another way to prevent the trapped particle instability is to taper the undulator. This should cause about half of the electrons to become untrapped, which would reduce the synchrotron oscillations. In Fig. 3, the undulator is given a 10% taper in resonant energy S = -4-n Ayly = 88 n. The average output power is increased to 43 W, but the power evolution P(n) shows significant oscillations. This may be due to sporadic attempts at sideband formation. The sideband growth is reduced significantly, and the spectral
0168.9002/96/$15,00 Copyright 0 1996 Elsevier Science B.V. All rights reserved SSDI 0168.9002(95)01187-O
J. Blnu et al.
4n
mn
I Nucl. Instr.
and Mrth.
o_=os
no=1
0&l
Og'l.4
68.1
0 =8.4 P
Nl220
a=0
no=o.5
Q=5
e-o.01
1080
0
358-359
359
rwolution
Wrap
j-1800
la(z.n)I
in Phvs. Res. A 375 (1996)
Pw,n)
la(x.n)
I
50
50
0
n
Fig. 2. Multi-pass
50 -201
evolution
v
2010
of the Boeing
n
50
1kW FEL oscillator.
0
n
50 -20.1
Fig. 3. The Boeing oscillator
"
2010
11
with a tapered undulator.
50
6 = 88-a.
Q =5.
width is now only AMA = 1%. Increasing the outcoupling or the system duty factor would be necessary to achieve I kW average power.
The authors
[Jl J. Adamski et al., white paper Space Group.
(1994)
Boeing
Defense
&
[21 W.B. Colson. in: Free Electron Laser Handbook, eds. W.B. Colson, C. Pellegrini and A. Renieri (Elsevier. Amsterdam, 1990) chap. 5.
Acknowledgements for support of this work by the School, and SURAICEBAF.
are grateful
Naval Postgraduate
References
[31 N.M. Kroll and M.N. Rosenbluth, Electronics, vol. 7 (1980) 147.
Physics
of Quantum
VI. HIGH POWER
FELs