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Theory and experiment for a new focusing wiggler
NUCLEAR INSTRUMENTS Sr METHODS IN PHYSICS RESEARCH
Nuclear Instruments and Methods in Physics Research A318 (1992) 834-838 North-Holland
SectionA
heorv and ..
~.t
ent for a new focusing wiggler
K. Mima a, T. Okazaki b, S. Sato ", Y. Tsunawaki d, K. Imasaki e, T. Akiba ", S. Kuruma `', M. Naruo e, Y. Hosoda ", Y. Kawata c, A. Kobayashi 1, S. Nakai a and C. Yamanaka °~ Institute of Laser Engineering, Osaka Unirersity, 2-6 Yantada-oka Suita, Osaka 565, Japan Stunitonto Elec. Ind., Osaka, Japan Mitsubishi Elec. Ind., Itand. Japan `t Osaka Satt fo UnirersiM Osaka, Japan Institute for Laser Teclinolof, Osaka, Japan K Steel Ltd., Osaka, Japan
Presented are the theoretical analysis and an experiment on a new wigglerwhich has a focusing field and tapering by a movable electromagnet . The electron beam propagation experiments show that a high emittance electron beam propagates with a relatively small beam radius . The gain for this wiggler is also investigated by the 3D FEL simulation code FUELNDES. l. Ininduction Recently, several designs of wigglers with focusing magnetic fields have been proposed [1-31. Some of them have the difficulty of a reduction of the gain because the transverse wiggler field is nonuniform. In this paper, we propose a new wiggler design which includes focusing forces in both horizontal and vertical directions and the wiggler field tapering by an additional electromagnet . The optimum beam radius which gives the maximum gain should be approximately A we /2-.r 2, where E is the normalized emittance and Aw the wiggler period. This requires that the betatron oscillation period A,, determined by the focusing force has to be yA w. This means that a stronger focusing force is required for a shorter wiggler period. For a fixed radiation wavelength A n , A ,3 /A w = (Aw/2A K-)1/-, where K is the wiggler parameter . Therefore, the focusing technique is in particular important for compact wigglers.
For a pitch angle 0 of an electron's wiggle motion and the edge angle a, the electron beam is focused on the axis horizontally when a > 0. However, the electron Table 1 Focusing conditions
Case
Electron Energy
Edge Angle a
A
g
a=0
I
i
Defocus
Focus
I I I
Focus
l C
Low
O
a=9
I I I I I I I
2. A new wiggler design
Elsevier Science Publishers B.V.
X-direction Y-direction
Î
D
The schematic diagram of our new wiggler is shown in fig. 1 . There are two unique ideas included in this wiggler . One of them is that the shape of the ion pole piece is trapedozoidal . The second is that the electromagnets are added to the outside of the Halbach-type wiggler in order to taper the wiggler field continuously . The horizontal (x-direction) and vertical (y-direction) focusing conditions are summarized in table 1 .
Focus and Defocus
Conditions
E
High
A
I I I
'
._
a al ,
Focus
Focus
Focus
-
Focus
Defocus
K. Mima et al. / Theory and experiment for a new focusing wiggler Permanent Magnet
Pole Place
P01e Piece
Magnetic Field
835
Electromagnet
Permanent \ Magnet
Electron Orbit
Fig . 1 . Schematic diagram of the new hybrid compact wiggler.
beam on the axis is defocused vertically when a > 0. Since 0 = k/y for the wiggler parameter K = eBw/ (k w inc 2 ), the vertical focus condition depends upon the electron beam energy and the K parameter . This is not convenient when we change the electron beam energy. We may improve this difficulty by combining three types of poles periodically. In this case, the beam can be focused on average in both directions for any beam energy . In order to vary the wiggler field along the axis, we change the gap between the main magnets and the electromagnets, and also the current of the electromag-
Table 2 Wiggler parameters Permanent magnet material Pole material Overall length Pole width Pole pitch Pole gap Pole angle Peak magnetic field K parameter Wavelength (at 4 MeV)
Nd-Fe-B pure ion 1000 mm 80 mm 20 mm 10 mm 1° 0.31 T 0.57 0.19 mm
3500 3
l7 N
I Tunable Range
3000
d rn
1 S t Gap
2500
Axis 4Wiggler -±+. 1 .0
2.0
3.0
4.0
5.0
'
Co
Gap Distance (mm) Fig . 2. Wiggler field control with electromagnet . X. UNDULATORS
K Mina et al. / Theory and experiment for a newfocusing wiggler
5
4
2
a
fte
Fig. 3. A photograph of the new wiggler.
Electron beam
0
415
Table 3 FEL parameters energy energy spread current radius angular spread
2.3 MeV 3% 200 A 2 mm 7 x 10-2 rad
Wiggler
wavelength number of periods K value
2 cm 50 0.57
Laser
wavelength radius
430 p.m 8 mm
420
425
430
Wavelength (gm)
435
440
Fig. 5. Gain curves for various edge angles .
nets. The field changes with the gap as shown in fig . 2. In the present wiggler, the magnetic field can change from 0.25 to 0.33 T. By chan, ing the current, the magnetic field can be varied by ± 100 G. This may be useful for the precise control of the wiggler field. Finally, the wiggler parameters are shown in table 2, and a photograph of the wiggler is shown in fig . 3.
10
Wiggler Period (z/Àw) Fig. 4. Spatial evolution of the electron beam envelope .
K Mina et al. / Theory and experiment for a newfocusing wiggler
837
using the 3D FEL simulation code FUELNDES, which was developed at the Institute of Laser Engineering, Osaka University, and the Institute for Laser Technology. The radius of the beam varies as shown in fig. 4
3. Gain and beam propagation experiment
The numerical analysis of the beam propagation and the amplification of radiation has been done by
Wiggler Magnet I
-200 -100
U
0
Wiggler Gap Beam Energy y
,
I
,
,
10.6 mm 6-7
-150
-50
0_
100
150
200
600
I
100 200 300 400 500 600 700 800 900 1000 1100 1200
700
250
890
1000
Fig. 6. Electron beam cross sections in the new wiggler. X. UNDULATORS
h'. Müna et al. / Titeury and experànent for a nen, focusing itiggier for the wiggler and beam parameters of table 3. Here, the magnetic field gradient is indicated in the figure in units of G/cm; dBw/dx corresponds to the edge angle. Roughly speaking, d Bw/dx = 7()a (degrees). The gains for various focusing forces are shown in fig- 5. In this example, the optimum d Bw/dx is 2(H1 G/cm which corresponds to a = 3°. The betatron length is approximately 20Aw . Conclusions and discussion A preliminary beam propagation experiment has been performed by using the induction linac. The result is shown in fig. 6, where the spatial evolution of the electron beam cross section is shown. This indicates that the electron beam is well confined to a small radius.
The numerical results show that focusing is essential for optimizing the amplification process. With the appropriate focusing, the gain is enhanced almost by one order of magnitude. The present focusing scheme will be compared with other focusing methods in the future in order to clarify advantages and disadvantages of this wiggler.
References [1] D.C. Quimby and J.M . Slater, in : Free-Electron Genera-
tors of Coherent Radiation, eds. C. Brau et al ., SPIE 452 (SPIE, Bellingham, WA, 1984). [2) E.T. Scharlemann, J. Appl . Phys. 58 (1985) 2154. [3) Y., Tunawaki et al., Nucl. Instr. and Meth . A304 (1991) 753.
Nuclear Instruments and Methods in Physics Research A318 (1992) 834-838 North-Holland
SectionA
heorv and ..
~.t
ent for a new focusing wiggler
K. Mima a, T. Okazaki b, S. Sato ", Y. Tsunawaki d, K. Imasaki e, T. Akiba ", S. Kuruma `', M. Naruo e, Y. Hosoda ", Y. Kawata c, A. Kobayashi 1, S. Nakai a and C. Yamanaka °~ Institute of Laser Engineering, Osaka Unirersity, 2-6 Yantada-oka Suita, Osaka 565, Japan Stunitonto Elec. Ind., Osaka, Japan Mitsubishi Elec. Ind., Itand. Japan `t Osaka Satt fo UnirersiM Osaka, Japan Institute for Laser Teclinolof, Osaka, Japan K Steel Ltd., Osaka, Japan
Presented are the theoretical analysis and an experiment on a new wigglerwhich has a focusing field and tapering by a movable electromagnet . The electron beam propagation experiments show that a high emittance electron beam propagates with a relatively small beam radius . The gain for this wiggler is also investigated by the 3D FEL simulation code FUELNDES. l. Ininduction Recently, several designs of wigglers with focusing magnetic fields have been proposed [1-31. Some of them have the difficulty of a reduction of the gain because the transverse wiggler field is nonuniform. In this paper, we propose a new wiggler design which includes focusing forces in both horizontal and vertical directions and the wiggler field tapering by an additional electromagnet . The optimum beam radius which gives the maximum gain should be approximately A we /2-.r 2, where E is the normalized emittance and Aw the wiggler period. This requires that the betatron oscillation period A,, determined by the focusing force has to be yA w. This means that a stronger focusing force is required for a shorter wiggler period. For a fixed radiation wavelength A n , A ,3 /A w = (Aw/2A K-)1/-, where K is the wiggler parameter . Therefore, the focusing technique is in particular important for compact wigglers.
For a pitch angle 0 of an electron's wiggle motion and the edge angle a, the electron beam is focused on the axis horizontally when a > 0. However, the electron Table 1 Focusing conditions
Case
Electron Energy
Edge Angle a
A
g
a=0
I
i
Defocus
Focus
I I I
Focus
l C
Low
O
a=9
I I I I I I I
2. A new wiggler design
Elsevier Science Publishers B.V.
X-direction Y-direction
Î
D
The schematic diagram of our new wiggler is shown in fig. 1 . There are two unique ideas included in this wiggler . One of them is that the shape of the ion pole piece is trapedozoidal . The second is that the electromagnets are added to the outside of the Halbach-type wiggler in order to taper the wiggler field continuously . The horizontal (x-direction) and vertical (y-direction) focusing conditions are summarized in table 1 .
Focus and Defocus
Conditions
E
High
A
I I I
'
._
a al ,
Focus
Focus
Focus
-
Focus
Defocus
K. Mima et al. / Theory and experiment for a new focusing wiggler Permanent Magnet
Pole Place
P01e Piece
Magnetic Field
835
Electromagnet
Permanent \ Magnet
Electron Orbit
Fig . 1 . Schematic diagram of the new hybrid compact wiggler.
beam on the axis is defocused vertically when a > 0. Since 0 = k/y for the wiggler parameter K = eBw/ (k w inc 2 ), the vertical focus condition depends upon the electron beam energy and the K parameter . This is not convenient when we change the electron beam energy. We may improve this difficulty by combining three types of poles periodically. In this case, the beam can be focused on average in both directions for any beam energy . In order to vary the wiggler field along the axis, we change the gap between the main magnets and the electromagnets, and also the current of the electromag-
Table 2 Wiggler parameters Permanent magnet material Pole material Overall length Pole width Pole pitch Pole gap Pole angle Peak magnetic field K parameter Wavelength (at 4 MeV)
Nd-Fe-B pure ion 1000 mm 80 mm 20 mm 10 mm 1° 0.31 T 0.57 0.19 mm
3500 3
l7 N
I Tunable Range
3000
d rn
1 S t Gap
2500
Axis 4Wiggler -±+. 1 .0
2.0
3.0
4.0
5.0
'
Co
Gap Distance (mm) Fig . 2. Wiggler field control with electromagnet . X. UNDULATORS
K Mina et al. / Theory and experiment for a newfocusing wiggler
5
4
2
a
fte
Fig. 3. A photograph of the new wiggler.
Electron beam
0
415
Table 3 FEL parameters energy energy spread current radius angular spread
2.3 MeV 3% 200 A 2 mm 7 x 10-2 rad
Wiggler
wavelength number of periods K value
2 cm 50 0.57
Laser
wavelength radius
430 p.m 8 mm
420
425
430
Wavelength (gm)
435
440
Fig. 5. Gain curves for various edge angles .
nets. The field changes with the gap as shown in fig . 2. In the present wiggler, the magnetic field can change from 0.25 to 0.33 T. By chan, ing the current, the magnetic field can be varied by ± 100 G. This may be useful for the precise control of the wiggler field. Finally, the wiggler parameters are shown in table 2, and a photograph of the wiggler is shown in fig . 3.
10
Wiggler Period (z/Àw) Fig. 4. Spatial evolution of the electron beam envelope .
K Mina et al. / Theory and experiment for a newfocusing wiggler
837
using the 3D FEL simulation code FUELNDES, which was developed at the Institute of Laser Engineering, Osaka University, and the Institute for Laser Technology. The radius of the beam varies as shown in fig. 4
3. Gain and beam propagation experiment
The numerical analysis of the beam propagation and the amplification of radiation has been done by
Wiggler Magnet I
-200 -100
U
0
Wiggler Gap Beam Energy y
,
I
,
,
10.6 mm 6-7
-150
-50
0_
100
150
200
600
I
100 200 300 400 500 600 700 800 900 1000 1100 1200
700
250
890
1000
Fig. 6. Electron beam cross sections in the new wiggler. X. UNDULATORS
h'. Müna et al. / Titeury and experànent for a nen, focusing itiggier for the wiggler and beam parameters of table 3. Here, the magnetic field gradient is indicated in the figure in units of G/cm; dBw/dx corresponds to the edge angle. Roughly speaking, d Bw/dx = 7()a (degrees). The gains for various focusing forces are shown in fig- 5. In this example, the optimum d Bw/dx is 2(H1 G/cm which corresponds to a = 3°. The betatron length is approximately 20Aw . Conclusions and discussion A preliminary beam propagation experiment has been performed by using the induction linac. The result is shown in fig. 6, where the spatial evolution of the electron beam cross section is shown. This indicates that the electron beam is well confined to a small radius.
The numerical results show that focusing is essential for optimizing the amplification process. With the appropriate focusing, the gain is enhanced almost by one order of magnitude. The present focusing scheme will be compared with other focusing methods in the future in order to clarify advantages and disadvantages of this wiggler.
References [1] D.C. Quimby and J.M . Slater, in : Free-Electron Genera-
tors of Coherent Radiation, eds. C. Brau et al ., SPIE 452 (SPIE, Bellingham, WA, 1984). [2) E.T. Scharlemann, J. Appl . Phys. 58 (1985) 2154. [3) Y., Tunawaki et al., Nucl. Instr. and Meth . A304 (1991) 753.