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Beam optical system of the polarized electron source of the Amsterdam pulse stretcher AmPS
Nuclear Instruments and Methods in Physics Research A 427 (1999) 46}50
Beam optical system of the polarized electron source of the Amsterdam pulse stretcher AmPS B.L. Militsyn *, P.W. van Amersfoort , I.A. Koop, V.Ya. Korchagin, G. Luijckx , N.H. Papadakis, G.V. Serdobintsev NIKHEF, Technical Physics, P.O. Box 41882, 1009 DB Amsterdam, The Netherlands BINP, 630090, Novosibirsk, Russia IASA, P.O. Box 17214, 10024 Athens, Greece
Abstract The beam optical system of a Polarized Electron Source (PES) is described. The PES is used for nuclear physics experiments with internal gas targets on the MEA-AmPS acceleration facility at NIKHEF. The PES beam optical system consists of a 100 keV photoelectron gun, a 100 keV beam line, and a 400 keV post-accelerator. Both the electrostatic and the beam trajectory calculations in the gun have been performed with the SAM code. To calculate the beam envelope in the PES beam line the MAD code was used. The input for MAD was obtained from beam trajectory calculations in the gun, extrapolated for a beam with non-zero initial emittance. Results of the beam line performance test are given. 1999 Elsevier Science B.V. All rights reserved. PACS: 29.25.B; 29.27.E; 29.27.H Keywords: AmPS; Electron; Optics; Polarization
1. Introduction The MEA-AmPS accelerator facility at NIKHEF [1] has two electron injectors } a 400 keV thermionic gun and a Polarized Electron Source (PES) [2]. The second one is used to provide spin-polarized electrons for nuclear physics experiments with internal gas targets. The PES (see Fig. 1) consists of
* Corresponding author.
a 100 keV photoelectron gun, a Z-shape spin manipulator, a Mott-polarimeter, and a 400 keV post-accelerator. A 2703 bending magnet (a-magnet), installed downstream from the post-accelerator, allows injection of electrons from PES into the linear Medium Energy Accelerator (MEA). When the a-magnet is switched o! electrons from the thermionic gun can be injected. The PES operates in a pulsed mode providing 2 ls long pulses of 400 keV electrons with a repetition rate of 1 Hz. The duration of the beam pulses and the repetition rate are determined by a Ti:Sapphire laser that
0168-9002/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 1 5 0 9 - 5
B.L. Militsyn et al. / Nuclear Instruments and Methods in Physics Research A 427 (1999) 46}50
47
Fig. 2. The beam trajectories in the photoelectron gun.
Fig. 1. General layout of the PES.
illuminates the photocathode. The current of the pulses in the MEA is typically of the order of 5 mA or higher.
Fig. 2 the calculated trajectories are shown for an electron beam with a current of 50 mA, and an emission surface diameter of 6 mm. The calculated rms beam emittance, originating from the nonlinearity of the electrical "eld of the electrode system and of space charge e!ects, does not exceed 1 mm mrad. The small variations of the beam envelope angle as a function of current at the gun exit are compensated by a solenoid lens Sgun installed after the gun.
2. The electron optical system of the photoelectron gun The primary source of the polarized electrons is a 100 keV photoelectron gun. Its design is based on a Pierce-type electrode optical system with an acceleration gap of 65 mm. The cathode assembly allows for the installation of a photocathode with an active diameter of 12 mm. The diameter of the emitting part of the photocathode (ED) is determined by the laser light spot diameter on its surface, which can be varied in the range of 1}7 mm. At an ED of 6 mm the maximum current, as determined by Child's law, is 360 mA. Normally the gun operates in a current range of 0}50 mA. To optimize focusing and to minimize non-linear e!ects, within this current range, a cathode electrode angle of 153 has been chosen. The electrode optical system was designed using the SAM-code [3]. In
3. Emittance calculation for a beam with non-zero initial temperature From the gun the polarized electrons are transported through a 8 m long beam line. To ensure a transport e$ciency close to 100% the diameter of the beam line pipes must be large enough to transport all electrons, provided by the gun, and small enough to minimize transport of residual gas to the ultrahigh vacuum gun chamber. To design a beam line we have to know the beam envelope with high precision. To calculate the beam envelope with codes like MAD, DIMAD or TRANSPORT we have to know the beam emittance at the beginning of the beam line and the initial Twiss parameters of the beam (a, b, c).
48
B.L. Militsyn et al. / Nuclear Instruments and Methods in Physics Research A 427 (1999) 46}50
Consider a model of an emission current distribution function with the spatial part of the distribution close to a Gaussian. The electrons are supposed to be emitted isotropically and their transverse velocity distribution to be Maxwellian. The 2-D distribution function is then 1 o(x, x )" e\V NV \VY NVY 2pp p V VY
(1)
where
k¹ p " VY 2mbcc and b and c relate to the longitudinal velocities of the electrons. A zero-order estimate of the beam emittance may be obtained by an rms emittance approach [4]. The rms emittance in this case is given by the expression: e "4p p . V VY The precision obtained by using the rms emittance is not su$cient for us. For example the rms emittance of a 2-D Gauss-like spatial distribution contains only 46.6% of the particles. Therefore, we calculated the emittance in a more direct way. The distribution function (1) was cut o! at a value C and a fraction of particles, contained inside the region, where o(x, x )'C was calculated. For the 2-D Gauss-like distribution function this region is an ellipse having the equation x x # "1. !2 ln(2Cpp p )p !2 ln(2Cpp p )p V VY V V VY VY If we want this ellipse to contain a fraction of particles N, its area or the beam emittance is determined by the formula: e"!2pp p ln(1!N). V VY For N"0.99 the value of emittance is e" 28.9p p which is much higher than the value estiV VY mated with the rms method. With the help of the SAM code we know the envelope parameters of the beam with zero initial temperature. If the behavior of the beam in the gun is linear, the beam emittance is determined by the e!ective temperature of the cathode only. Consider the beam position on the phase space of one spatial
direction before and after acceleration in the gun. During calculation with the SAM code it is assumed that the electrons are initially distributed along a straight line +(!r, 0), (r, 0), and do not have transverse momenta. During acceleration the relative positions of the particles along a straight line do not change, and the beam phase volume transforms into a straight line +(!x ,!x ), (x , x ),, where r is the cathode radius, x and x are the radius and angle of the beam envelope at the gun exit. The emittance of the beam e is estimated by using the approach described before. Suppose that the straight line +(!x ,!x ), (x , x ), is an axis of an ellipse with area e. Then the Twiss parameter b of the beam is the root of the equation (be x " . (1#(x /bx ) The parameters a and c are calculated according to the formulae: a"x /(bx )!bx /x , and c" (1#a)/b. These parameters are used as the input for MAD.
4. Optics of the 100 keV beam line The 100 keV beam line consists of by the 903 magnetic bend, the Z-manipulator and the transport section. The 903 bend consists of a pair of 453 bending magnets BM101 and BM102 with edge focusing and a straight section in between. To obtain identical focusing properties of the bend in both horizontal and vertical directions, the optimal ratio between the straight section length S and the bending radius R is S/R"4.41345 with an edge angle of 11.643. The transport matrix for both directions is then given by
!0.9966
4.416R
.
!0.001553R\ !0.9966
The 903 magnetic bend de#ects the electron beam from the optical axis of the laser system and directs it to the Z-manipulator. Two solenoids S101 and S102 focus the beam at the entrance of the
B.L. Militsyn et al. / Nuclear Instruments and Methods in Physics Research A 427 (1999) 46}50
49
to avoid an additional coupling these solenoids have equal currents with opposite polarities. Two spin rotating solenoids S104 and S105 are installed close and symmetrically around the beam waist and provide azimuth spin rotation de"ned by the formula ge
" 2cmv
Fig. 3. Spin orientation in the Z-manipulator.
electrostatic de#ector EB101. To prevent horizontal}vertical coupling, they have identical "eld strengths and opposite "eld directions. The Z-manipulator [5] is included in the PES beam line to allow full rotation of the polarization vector over the solid angle of 4p. It consists of two electrostatic de#ectors EB101 and EB102 and two spin rotating sections for the polar angle (S103S106) and for the azimuth angle (S107-S110) (see Fig. 3). After leaving the photocathode, the electron spin vector is parallel to the momentum vector of the particle and at low energy it follows this direction in a magnetic "eld. The "rst electrostatic de#ector EB101 bends the beam by 107.73. According to the BMT equation [6] after passing such a de#ector the spin vector of a 100 keV electron lays in the horizontal plane and is oriented perpendicular to the momentum vector. The spin rotation section consists of four solenoids. Solenoids S103 and S106 transport the beam from the output of the electrostatic de#ector EB101 to the input of the de#ector EB102. There is a beam waist in the middle of the straight section. To prevent loss of control of the spin rotation and
B dl. J
Because of their location these solenoids do not disturb the beam transport and their in#uence may be easily compensated for with the transport solenoids. The design of the second spin rotation section is identical to the "rst one. The electrostatic de#ector EB102 bends the beam by 107.73. The vertical component of the spin vector is not changed while the horizontal component is rotated by an angle of 903 with respect to the momentum vector. So after passing the de#ector the horizontal component of the spin vector is oriented parallel to the momentum vector. The required azimuthal angle may be set by the pair of solenoids S108 and S109. The transport solenoids S107 and S110 focus the beam on the focal plane of the Mott-polarimeter. The transport section consists of the pair of solenoids S111 and S112 and determines the beam radius and the beam envelope angle at the entrance of the cavity C1 of the postaccelerator (PA). The solenoid lens S113 transports the beam through the cavity C2. Lens S114 focuses the beam either on the entrance of prebuncher of the linac (operational mode) or on the Faraday cup installed behind the a-magnet (tune up mode). The PES beam line has been designed with the MAD code [7]. The results of the beam trajectory calculations in the gun, extrapolated for a beam with "nite initial emittance, were used as input for MAD.
5. The beam line test This electron optical system allows the transport of the 100 keV electron beam up to a distance of 8 m through the PES beam line and has a measured transmission of more than 99%. Fig. 4 shows an
50
B.L. Militsyn et al. / Nuclear Instruments and Methods in Physics Research A 427 (1999) 46}50
These experimental tests con"rm the results of the gun-beamline optics calculation and design and prove that the required beam parameters have been achieved.
References
Fig. 4. Laser pulse and the beam current pulse observed at three di!erent points of the PES beam line.
oscillogram of the 30 mA electron current in the PES beam line, observed at three points: in the center of the 903 magnetic bend (CM101), in the center of the transport section (CM102) and at the end of the beam line on the Faraday cup.
[1] G. Luijckx et al., Proccedings of the 1995 Particle Accelerator Conference, Dallas, p. 330. [2] Y.B. Bolkhovityanov et al., SPIN96 Proceedings, 1997, ISBN 981-02-3052-4. [3] M.A. Tiunov, B.M. Fomel, V.P. Yakovlev, Preprint BINP 89-159, Novosibirsk, 1989. [4] J.D. Lawson, The Physics of Charged Particle Beams, Oxford University Press, Oxford, 1997. [5] D.A. Engwall et al., Nucl. Instr. and Meth. A 324 (1993) 409. [6] V. Bargman, L. Michel, V.L. Telegdy, Phys. Rev. Lett. 2 (1959) 435. [7] H. Grote, F.C. Iselin, CERN/SL/90-13(AP).
Beam optical system of the polarized electron source of the Amsterdam pulse stretcher AmPS B.L. Militsyn *, P.W. van Amersfoort , I.A. Koop, V.Ya. Korchagin, G. Luijckx , N.H. Papadakis, G.V. Serdobintsev NIKHEF, Technical Physics, P.O. Box 41882, 1009 DB Amsterdam, The Netherlands BINP, 630090, Novosibirsk, Russia IASA, P.O. Box 17214, 10024 Athens, Greece
Abstract The beam optical system of a Polarized Electron Source (PES) is described. The PES is used for nuclear physics experiments with internal gas targets on the MEA-AmPS acceleration facility at NIKHEF. The PES beam optical system consists of a 100 keV photoelectron gun, a 100 keV beam line, and a 400 keV post-accelerator. Both the electrostatic and the beam trajectory calculations in the gun have been performed with the SAM code. To calculate the beam envelope in the PES beam line the MAD code was used. The input for MAD was obtained from beam trajectory calculations in the gun, extrapolated for a beam with non-zero initial emittance. Results of the beam line performance test are given. 1999 Elsevier Science B.V. All rights reserved. PACS: 29.25.B; 29.27.E; 29.27.H Keywords: AmPS; Electron; Optics; Polarization
1. Introduction The MEA-AmPS accelerator facility at NIKHEF [1] has two electron injectors } a 400 keV thermionic gun and a Polarized Electron Source (PES) [2]. The second one is used to provide spin-polarized electrons for nuclear physics experiments with internal gas targets. The PES (see Fig. 1) consists of
* Corresponding author.
a 100 keV photoelectron gun, a Z-shape spin manipulator, a Mott-polarimeter, and a 400 keV post-accelerator. A 2703 bending magnet (a-magnet), installed downstream from the post-accelerator, allows injection of electrons from PES into the linear Medium Energy Accelerator (MEA). When the a-magnet is switched o! electrons from the thermionic gun can be injected. The PES operates in a pulsed mode providing 2 ls long pulses of 400 keV electrons with a repetition rate of 1 Hz. The duration of the beam pulses and the repetition rate are determined by a Ti:Sapphire laser that
0168-9002/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 1 5 0 9 - 5
B.L. Militsyn et al. / Nuclear Instruments and Methods in Physics Research A 427 (1999) 46}50
47
Fig. 2. The beam trajectories in the photoelectron gun.
Fig. 1. General layout of the PES.
illuminates the photocathode. The current of the pulses in the MEA is typically of the order of 5 mA or higher.
Fig. 2 the calculated trajectories are shown for an electron beam with a current of 50 mA, and an emission surface diameter of 6 mm. The calculated rms beam emittance, originating from the nonlinearity of the electrical "eld of the electrode system and of space charge e!ects, does not exceed 1 mm mrad. The small variations of the beam envelope angle as a function of current at the gun exit are compensated by a solenoid lens Sgun installed after the gun.
2. The electron optical system of the photoelectron gun The primary source of the polarized electrons is a 100 keV photoelectron gun. Its design is based on a Pierce-type electrode optical system with an acceleration gap of 65 mm. The cathode assembly allows for the installation of a photocathode with an active diameter of 12 mm. The diameter of the emitting part of the photocathode (ED) is determined by the laser light spot diameter on its surface, which can be varied in the range of 1}7 mm. At an ED of 6 mm the maximum current, as determined by Child's law, is 360 mA. Normally the gun operates in a current range of 0}50 mA. To optimize focusing and to minimize non-linear e!ects, within this current range, a cathode electrode angle of 153 has been chosen. The electrode optical system was designed using the SAM-code [3]. In
3. Emittance calculation for a beam with non-zero initial temperature From the gun the polarized electrons are transported through a 8 m long beam line. To ensure a transport e$ciency close to 100% the diameter of the beam line pipes must be large enough to transport all electrons, provided by the gun, and small enough to minimize transport of residual gas to the ultrahigh vacuum gun chamber. To design a beam line we have to know the beam envelope with high precision. To calculate the beam envelope with codes like MAD, DIMAD or TRANSPORT we have to know the beam emittance at the beginning of the beam line and the initial Twiss parameters of the beam (a, b, c).
48
B.L. Militsyn et al. / Nuclear Instruments and Methods in Physics Research A 427 (1999) 46}50
Consider a model of an emission current distribution function with the spatial part of the distribution close to a Gaussian. The electrons are supposed to be emitted isotropically and their transverse velocity distribution to be Maxwellian. The 2-D distribution function is then 1 o(x, x )" e\V NV \VY NVY 2pp p V VY
(1)
where
k¹ p " VY 2mbcc and b and c relate to the longitudinal velocities of the electrons. A zero-order estimate of the beam emittance may be obtained by an rms emittance approach [4]. The rms emittance in this case is given by the expression: e "4p p . V VY The precision obtained by using the rms emittance is not su$cient for us. For example the rms emittance of a 2-D Gauss-like spatial distribution contains only 46.6% of the particles. Therefore, we calculated the emittance in a more direct way. The distribution function (1) was cut o! at a value C and a fraction of particles, contained inside the region, where o(x, x )'C was calculated. For the 2-D Gauss-like distribution function this region is an ellipse having the equation x x # "1. !2 ln(2Cpp p )p !2 ln(2Cpp p )p V VY V V VY VY If we want this ellipse to contain a fraction of particles N, its area or the beam emittance is determined by the formula: e"!2pp p ln(1!N). V VY For N"0.99 the value of emittance is e" 28.9p p which is much higher than the value estiV VY mated with the rms method. With the help of the SAM code we know the envelope parameters of the beam with zero initial temperature. If the behavior of the beam in the gun is linear, the beam emittance is determined by the e!ective temperature of the cathode only. Consider the beam position on the phase space of one spatial
direction before and after acceleration in the gun. During calculation with the SAM code it is assumed that the electrons are initially distributed along a straight line +(!r, 0), (r, 0), and do not have transverse momenta. During acceleration the relative positions of the particles along a straight line do not change, and the beam phase volume transforms into a straight line +(!x ,!x ), (x , x ),, where r is the cathode radius, x and x are the radius and angle of the beam envelope at the gun exit. The emittance of the beam e is estimated by using the approach described before. Suppose that the straight line +(!x ,!x ), (x , x ), is an axis of an ellipse with area e. Then the Twiss parameter b of the beam is the root of the equation (be x " . (1#(x /bx ) The parameters a and c are calculated according to the formulae: a"x /(bx )!bx /x , and c" (1#a)/b. These parameters are used as the input for MAD.
4. Optics of the 100 keV beam line The 100 keV beam line consists of by the 903 magnetic bend, the Z-manipulator and the transport section. The 903 bend consists of a pair of 453 bending magnets BM101 and BM102 with edge focusing and a straight section in between. To obtain identical focusing properties of the bend in both horizontal and vertical directions, the optimal ratio between the straight section length S and the bending radius R is S/R"4.41345 with an edge angle of 11.643. The transport matrix for both directions is then given by
!0.9966
4.416R
.
!0.001553R\ !0.9966
The 903 magnetic bend de#ects the electron beam from the optical axis of the laser system and directs it to the Z-manipulator. Two solenoids S101 and S102 focus the beam at the entrance of the
B.L. Militsyn et al. / Nuclear Instruments and Methods in Physics Research A 427 (1999) 46}50
49
to avoid an additional coupling these solenoids have equal currents with opposite polarities. Two spin rotating solenoids S104 and S105 are installed close and symmetrically around the beam waist and provide azimuth spin rotation de"ned by the formula ge
" 2cmv
Fig. 3. Spin orientation in the Z-manipulator.
electrostatic de#ector EB101. To prevent horizontal}vertical coupling, they have identical "eld strengths and opposite "eld directions. The Z-manipulator [5] is included in the PES beam line to allow full rotation of the polarization vector over the solid angle of 4p. It consists of two electrostatic de#ectors EB101 and EB102 and two spin rotating sections for the polar angle (S103S106) and for the azimuth angle (S107-S110) (see Fig. 3). After leaving the photocathode, the electron spin vector is parallel to the momentum vector of the particle and at low energy it follows this direction in a magnetic "eld. The "rst electrostatic de#ector EB101 bends the beam by 107.73. According to the BMT equation [6] after passing such a de#ector the spin vector of a 100 keV electron lays in the horizontal plane and is oriented perpendicular to the momentum vector. The spin rotation section consists of four solenoids. Solenoids S103 and S106 transport the beam from the output of the electrostatic de#ector EB101 to the input of the de#ector EB102. There is a beam waist in the middle of the straight section. To prevent loss of control of the spin rotation and
B dl. J
Because of their location these solenoids do not disturb the beam transport and their in#uence may be easily compensated for with the transport solenoids. The design of the second spin rotation section is identical to the "rst one. The electrostatic de#ector EB102 bends the beam by 107.73. The vertical component of the spin vector is not changed while the horizontal component is rotated by an angle of 903 with respect to the momentum vector. So after passing the de#ector the horizontal component of the spin vector is oriented parallel to the momentum vector. The required azimuthal angle may be set by the pair of solenoids S108 and S109. The transport solenoids S107 and S110 focus the beam on the focal plane of the Mott-polarimeter. The transport section consists of the pair of solenoids S111 and S112 and determines the beam radius and the beam envelope angle at the entrance of the cavity C1 of the postaccelerator (PA). The solenoid lens S113 transports the beam through the cavity C2. Lens S114 focuses the beam either on the entrance of prebuncher of the linac (operational mode) or on the Faraday cup installed behind the a-magnet (tune up mode). The PES beam line has been designed with the MAD code [7]. The results of the beam trajectory calculations in the gun, extrapolated for a beam with "nite initial emittance, were used as input for MAD.
5. The beam line test This electron optical system allows the transport of the 100 keV electron beam up to a distance of 8 m through the PES beam line and has a measured transmission of more than 99%. Fig. 4 shows an
50
B.L. Militsyn et al. / Nuclear Instruments and Methods in Physics Research A 427 (1999) 46}50
These experimental tests con"rm the results of the gun-beamline optics calculation and design and prove that the required beam parameters have been achieved.
References
Fig. 4. Laser pulse and the beam current pulse observed at three di!erent points of the PES beam line.
oscillogram of the 30 mA electron current in the PES beam line, observed at three points: in the center of the 903 magnetic bend (CM101), in the center of the transport section (CM102) and at the end of the beam line on the Faraday cup.
[1] G. Luijckx et al., Proccedings of the 1995 Particle Accelerator Conference, Dallas, p. 330. [2] Y.B. Bolkhovityanov et al., SPIN96 Proceedings, 1997, ISBN 981-02-3052-4. [3] M.A. Tiunov, B.M. Fomel, V.P. Yakovlev, Preprint BINP 89-159, Novosibirsk, 1989. [4] J.D. Lawson, The Physics of Charged Particle Beams, Oxford University Press, Oxford, 1997. [5] D.A. Engwall et al., Nucl. Instr. and Meth. A 324 (1993) 409. [6] V. Bargman, L. Michel, V.L. Telegdy, Phys. Rev. Lett. 2 (1959) 435. [7] H. Grote, F.C. Iselin, CERN/SL/90-13(AP).