- Email: [email protected]
Simulation of an annular beam free-electron laser
Nuclear
Instruments
and Methods
in Physics
Research
A 375
( 1996) 169-170
NUCLEAR INSTRUMENTS a METHODS IN PHYSICS RESEARCH SectIon A
Simulation of an annular beam free-electron M. Blank*, H.P. Freund’,
laser
R.H. Jackson, D.E. Pershing2, J.M. Taccetti’
Naval Research Laboratory,
Wa.shirrgton, DC -70.375, USA
Abstract A nonlinear analysis of an annular beam FEL with a helical wiggler and axial guide field is presented. An annular beam has the advantage of reduced DC self-fields, facilitating beam transport in short period wigglers. A 55 kV/5 A annular beam interacting with the TE, , cylindrical waveguide mode is considered. The inner and outer beam radii are 0.27 and 0.33 cm, respectively. The wiggler amplitude is 250 G and the period is 0.9 cm. Axial guide fields up to 3 kG are studied. The ARACHNE slow-time-scale simulation code shows that efficiencies of 10%. corresponding to gains >40 dB, are possible for grazing incidence with the TE, , mode in Ku-band. In addition, the 3 dB instantaneous bandwidth is found to be greater than 20%.
1. Introduction The free-electron laser (FEL) operation is based on the beating of the wiggler and radiation fields to produce a slowly varying ponderomotive wave in phase with the electron beam. The resonant wavelength depends upon the beam energy and the wiggler parameters as A = (I + ui &,/2y$ where A, is the wiggler period, x, is the bulk relativistic factor of the beam, and a,, = 0.0934BWh, for a wiggler amplitude BW in kG and period in cm. The wavelength, gain, and efficiency all decrease as the energy increases for fixed wiggler parameters. A great deal of effort has been devoted to the design of short period wigglers for high frequency operation with low beam energies. However. this is a self-defeating process since reductions in the wiggler period often result in reductions in the wiggler amplitude with a deleterious impact on the efficiency and gain. In order to circumvent these restrictions, we consider the effect of using an annular electron beam. This has the advantage that the DC self-fields are smaller than in a solid beam of comparable current, which facilities propagation through the small gaps required of short period wigglers. This configuration
is simulated
using
the ARACHNE
code
* Corresponding author. Tel. + I 202 767 6656, fax + I 202 767 1280, e-mail [email protected]. ’ Permanent address: Science Applications International Corp.. McLean. VA 22 102. ’ Permanent address: Mission Research Corp.. Newington. VA 22122. ‘Permanentaddress: University of Maryland, College Park, MD 20742. 0168-9002/96/$15.00 Copyright PIf SO168-9002(96)00045-9
[I,21 which is a slow-time-scale amplifier formulation which describes the interaction of the beam propagating through a helical wiggler and an axial guide field with the modes in a cylindrical waveguide and includes collective effects both in the beam-space-charge waves (i.e., Raman effects) and in the DC self-electric and self-magnetic fields due to the bulk beam charge and current densities.
2. Simulation
results
The ARACHNE code was used to simulate the performance of an annular beam FEL amplifier with a helical wiggler and an axial guide field. The device parameters, which correspond to grazing incidence for the fundamental TE, , mode, are listed in Table 1. The theoretical prediction of efficiency versus frequency for an ideal beam (energy spread AA; = 0) interacting with the TE, , cylindrical waveguide mode is plotted in Fig. 1. The simulation shows a peak efficiency of 10.6% and a 3 dB bandwidth of 22%. The degradation of peak efTable 1 Nominal design parameters Beam voltage Beam current Waveguide radius Wiggler period Wiggler field amplitude Axial guide field amplitude Centre frequency Input power
for the Ku-band
annular beam FEL 55 kV SA 0.6 cm 0.9 cm 0.25 kG 3 kG 17.0 GHz 1w
0 1996 Elsevier Science B.V. All rights reserved IV. LONG WAVELENGTH
FELs
hf. Blank et al.
170
ot,“““,.““,“““‘.” 14
IS
16
I Nucl. Instr.
17
18
arzd Meth.
in Phys. Rrs. A 375 (1996)
169-170
19
Frequency (GHz) Fig. I Theoretical predictions of efficiency versus frequency for a 55 kV/5 A electron beam interacting the a TE,, mode in the presence of a helical wiggler with 250 G magnetic field on axis.
Fig. 3. Comparison of output power versus interaction length for an annular electron beam (inner and outer radii of 0.27 cm and 0.33 cm, respectively), shown with the solid line, and a solid beam (0.3 cm radius). shown with the dashed line.
0.33 cm, while the radius of the radius of the solid beam was 0.3 cm. For both cases self fields were included and the energy spread was assumed to be zero. Fig. 3 shows that the annular beam interaction offers dramatic performance improvements over the solid beam. The saturated power for the annular beam interaction is more than twice that of the solid beam case. In addition. the saturation length is significantly reduced for the hollow beam, indicating that a shorter device is possible. 0
0.05
0.1
0.15
0.2
0.25
0.3
Av,lr,W
Fig. 2. Theoretical velocity spread.
predictions
of peak efficiency
versus
axial
ficiency with increasing axial energy spread is shown in Fig. 2. At an energy spread Ay,lx = 0.2%. the peak efficiency is reduced to approximately 4%, which is less than half the peak efficiency for an ideal beam. Thus, it is important to keep energy spread extremely low. The performance predictions for the annular beam interaction were compared to simulations for a solid beam interaction and the results are shown in Fig. 3. In the simulations, the total current, voltage, and wiggler field were held constant. The annular beam was assumed to have an inner radius of 0.27 cm and an outer radius of
Acknowledgements This work was supported by the Office of Naval Research. The computational work was supported in part by a grant of HPC time from the DOD HPC Center NAVO on a CRAY C90.
References [I] H.P. Freund and T.M. Antonsen. Jr., Principles of Freeelectron Lasers (Chapman & Hall, London, 1992) Chap. 5. [2] H.P. Freund, R.H. Jackson and D.E. Pershing. Phys. Fluids B5 (1993) 2318.
Instruments
and Methods
in Physics
Research
A 375
( 1996) 169-170
NUCLEAR INSTRUMENTS a METHODS IN PHYSICS RESEARCH SectIon A
Simulation of an annular beam free-electron M. Blank*, H.P. Freund’,
laser
R.H. Jackson, D.E. Pershing2, J.M. Taccetti’
Naval Research Laboratory,
Wa.shirrgton, DC -70.375, USA
Abstract A nonlinear analysis of an annular beam FEL with a helical wiggler and axial guide field is presented. An annular beam has the advantage of reduced DC self-fields, facilitating beam transport in short period wigglers. A 55 kV/5 A annular beam interacting with the TE, , cylindrical waveguide mode is considered. The inner and outer beam radii are 0.27 and 0.33 cm, respectively. The wiggler amplitude is 250 G and the period is 0.9 cm. Axial guide fields up to 3 kG are studied. The ARACHNE slow-time-scale simulation code shows that efficiencies of 10%. corresponding to gains >40 dB, are possible for grazing incidence with the TE, , mode in Ku-band. In addition, the 3 dB instantaneous bandwidth is found to be greater than 20%.
1. Introduction The free-electron laser (FEL) operation is based on the beating of the wiggler and radiation fields to produce a slowly varying ponderomotive wave in phase with the electron beam. The resonant wavelength depends upon the beam energy and the wiggler parameters as A = (I + ui &,/2y$ where A, is the wiggler period, x, is the bulk relativistic factor of the beam, and a,, = 0.0934BWh, for a wiggler amplitude BW in kG and period in cm. The wavelength, gain, and efficiency all decrease as the energy increases for fixed wiggler parameters. A great deal of effort has been devoted to the design of short period wigglers for high frequency operation with low beam energies. However. this is a self-defeating process since reductions in the wiggler period often result in reductions in the wiggler amplitude with a deleterious impact on the efficiency and gain. In order to circumvent these restrictions, we consider the effect of using an annular electron beam. This has the advantage that the DC self-fields are smaller than in a solid beam of comparable current, which facilities propagation through the small gaps required of short period wigglers. This configuration
is simulated
using
the ARACHNE
code
* Corresponding author. Tel. + I 202 767 6656, fax + I 202 767 1280, e-mail [email protected]. ’ Permanent address: Science Applications International Corp.. McLean. VA 22 102. ’ Permanent address: Mission Research Corp.. Newington. VA 22122. ‘Permanentaddress: University of Maryland, College Park, MD 20742. 0168-9002/96/$15.00 Copyright PIf SO168-9002(96)00045-9
[I,21 which is a slow-time-scale amplifier formulation which describes the interaction of the beam propagating through a helical wiggler and an axial guide field with the modes in a cylindrical waveguide and includes collective effects both in the beam-space-charge waves (i.e., Raman effects) and in the DC self-electric and self-magnetic fields due to the bulk beam charge and current densities.
2. Simulation
results
The ARACHNE code was used to simulate the performance of an annular beam FEL amplifier with a helical wiggler and an axial guide field. The device parameters, which correspond to grazing incidence for the fundamental TE, , mode, are listed in Table 1. The theoretical prediction of efficiency versus frequency for an ideal beam (energy spread AA; = 0) interacting with the TE, , cylindrical waveguide mode is plotted in Fig. 1. The simulation shows a peak efficiency of 10.6% and a 3 dB bandwidth of 22%. The degradation of peak efTable 1 Nominal design parameters Beam voltage Beam current Waveguide radius Wiggler period Wiggler field amplitude Axial guide field amplitude Centre frequency Input power
for the Ku-band
annular beam FEL 55 kV SA 0.6 cm 0.9 cm 0.25 kG 3 kG 17.0 GHz 1w
0 1996 Elsevier Science B.V. All rights reserved IV. LONG WAVELENGTH
FELs
hf. Blank et al.
170
ot,“““,.““,“““‘.” 14
IS
16
I Nucl. Instr.
17
18
arzd Meth.
in Phys. Rrs. A 375 (1996)
169-170
19
Frequency (GHz) Fig. I Theoretical predictions of efficiency versus frequency for a 55 kV/5 A electron beam interacting the a TE,, mode in the presence of a helical wiggler with 250 G magnetic field on axis.
Fig. 3. Comparison of output power versus interaction length for an annular electron beam (inner and outer radii of 0.27 cm and 0.33 cm, respectively), shown with the solid line, and a solid beam (0.3 cm radius). shown with the dashed line.
0.33 cm, while the radius of the radius of the solid beam was 0.3 cm. For both cases self fields were included and the energy spread was assumed to be zero. Fig. 3 shows that the annular beam interaction offers dramatic performance improvements over the solid beam. The saturated power for the annular beam interaction is more than twice that of the solid beam case. In addition. the saturation length is significantly reduced for the hollow beam, indicating that a shorter device is possible. 0
0.05
0.1
0.15
0.2
0.25
0.3
Av,lr,W
Fig. 2. Theoretical velocity spread.
predictions
of peak efficiency
versus
axial
ficiency with increasing axial energy spread is shown in Fig. 2. At an energy spread Ay,lx = 0.2%. the peak efficiency is reduced to approximately 4%, which is less than half the peak efficiency for an ideal beam. Thus, it is important to keep energy spread extremely low. The performance predictions for the annular beam interaction were compared to simulations for a solid beam interaction and the results are shown in Fig. 3. In the simulations, the total current, voltage, and wiggler field were held constant. The annular beam was assumed to have an inner radius of 0.27 cm and an outer radius of
Acknowledgements This work was supported by the Office of Naval Research. The computational work was supported in part by a grant of HPC time from the DOD HPC Center NAVO on a CRAY C90.
References [I] H.P. Freund and T.M. Antonsen. Jr., Principles of Freeelectron Lasers (Chapman & Hall, London, 1992) Chap. 5. [2] H.P. Freund, R.H. Jackson and D.E. Pershing. Phys. Fluids B5 (1993) 2318.