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A high-current beam transport facility for hollow beams
Vacuum/volume 34/numbers 1-2/pages 11 to 15/1984 Printed in Great Britain
0042-207X/84S3.00+.O0 Pergamon Press Ltd
A high-current beam transport facility for hollow beams P Krejcik, Kernforschungsanlage, JiJlich, W Germany and R Keller, Gesellschaft fdr Schwerionenforschung, Darmstadt, W Germany
A test experiment is reported in which a hollow beam is transported using a focusing system based on electrostatic coaxial lenses. The principle of this focusing system is described and design formulae given for the space charge limited current, which predict higher beam currents than with conventional focusing systems. Experimental beam measurements are presented together with results of computed space charge simulation in the beam, and matching conditions for the beam are described.
i. Introduction At low energies, beam brightness is generally limited through space-charge effects. High currents can be transported if the beam is fully space-charge neutralized, but this is only possible in the absence of electric fields. In the acceleration process, therefore, space charge forces in the beam will limit the current. The upper limit to the current is determined by the strength of the focusing forces available to balance the space charge forces. At low energies there are problems in providing strong focusing. The low particle velocities, particularly for heavy ions, reduce the efficiency of magnetic quadrupoles, and electric quadrupoles are also limited in strength by the aperture to length requirements and by the maximum electric field strength set by sparking. A new system I has been proposed that uses electrostatic coaxial cylinder lenses to provide strong focusing for hollow beams. In this system the space charge density is reduced by distributing ihe beam over a large annular aperture, but at the same time the focusing strength is maintained by the radial electric field between the inner and outer lens cylinders. In this way, the space-charge limited current of the transport system is raised beyond that of conventional, axial transport systems, as will be further described below. This feature of the hollow beam system makes it attractivefor consideration as a high-brightnessinjectorfor large,high-energy machines such as the spallationneutron source accelerator,and a possible future heavy-ion driver accelerator for inertialconfinement fusion. This is particularly so since the coaxial focusing principle for hollow beams can also be extended to a continuous focusing radio frequency linearaccelerator2.This rfstructure can bunch and acceleratea beam directlyfrom the ion source,thereby avoiding difficultieswith high-voltage dc accelerators for high currents. The favourable beam properties,as well as the simple construction of coaxial focusing elements, lend themselves also to more general applications of low-energy ion beam technology.
The ability to correct spherical and chromatic aberrations in finalfocus coaxial lenses 3 further extends the applications to microbeam technology. A hollow beam facility has been commissioned at GSI to test the beam transport characteristics of the coaxial focusing system. It accepts a beam of up to 50 keV of heavy ions from the highcurrent ion source CORDIS 4 and transports it through a periodic focusing system to a beam diagnostics chamber where beam emittance measurements can be made. The principle of the periodic focusing system is discussed in the next section, followed by a description of the facility. Beam measurements that have so far been made are compared to computer simulations of the beam-forming system.
2. Strong focusing of hollow beams with coaxial lenses The radial electric field between coaxial cylinders acts transversely on a hollow beam, deflecting it either toward or away from the axis depending on the sign of the applied field. The 1/r dependence of the electric field does not cause linear focusing about the lens axis. However, in a periodic system made up of converging and diverging lenses, as shown in Figure 1, the focusing is linear about the equilibrium path taken by the beam. This linear focusing gradient acts across the radial width, or thickness, of the hollow beam. The focusing field seen by the beam is diverging when the beam is deflected toward the axis and converging during deflection away from this axis. The focusing action is also characterized by the motion, in the r - r ' plane, of the panicles' co-ordinates at the end of each focusing period. In the r - r ' plane the particles trace out eigenellipses centred on a fixed point corresponding to the equilibrium trajectory, as shown in Figure 2. The sectional radial emittance, t,, of the beam can be represented by the area of such an ellipse, displaced from the origin, in the r - r ' plane. 11
A high-current beam transport facility for hollow beams
P Krejcik and R Keller:
eq~iibrium trajectory \.
for particles of velocity tic and where
÷
Io = 4neomoca/q" 3.1 x I 0 ~ A / Z [ a m p e r e s ] .
Figure i. Strong, alternating-gradient focusing for hollow beams is provided by the radial electric field between coaxial cylinders. The trajectories shown are for a periodically focused beam in a defocusing focusing cell.
eigen-ettipse
.
This current limit is a factor 2R/b greater than that given by Reiser 6 for periodic focusing of conventional, axial beams, where the sectional radial emittance and acceptance in equation (3) are replaced by their corresponding quantities in the axial beam case. The factor 2Rib does not, however, imply that the current limit can be increased indefinitely by making the beam large in radius and narrow in section since the focusing phase advance given by equation (1) also decreases with R. On the other hand, ooo0 cannot exceed the 2n stop-band, and for beam stability reasons 7 it should even be kept below n/2. Taking this additional boundary condition into account, the coaxial system is able to transport considerably more current than axial systems, as we shall see in the specific design example in the next section.
3. The hollow beam test stand
",,--
fixed poin~" / ~ ' ~ I I f I r~dius r
R
Figure 2. The r - r' plane of the hollow beam phase space. The fixed point corresponds to the equilibrium orbit of a periodically focused beam. Adjacent trajectories tracc out ellipses as they pass through consecutive cells. The area of the large possible ellipse is the sectional radial acceptance, =,, of the structure. The strength of the focusing is given by the normalized angular advance the particle makes around the eigen-ellipse after each focusing period. This focusing phase advance per cell can be readily calculated to first order, from a knowledge of the electric field strength at the average radius R = (% + r3/2 of the beam. For a particle potential W and a lens potential V~ this is given by
V~LD
(1)
aooo = 2 w R 2 In ro/ri where lenses of length L have spacing D between their centres; r o and r~ are the outer and inner lens cylinder radii and b = ( t o - r3/2. A point to note is that the potential on the diverging and converging lenses cannot have the same magnitude if the equilibrium trajectory has an average radius halfway between the inner and outer cylinders. This is due to the reduction in the electric field in the diverging lens where the trajectory radius is maximum. The sectional radial acceptance, ~,, of a focusing cell of length S is given by the area of the largest possible eigen-ellipse in the r - r' plane and is
[2)
=, = aooob2/S.
The space charge limited current in a transport channel is reached when the restoring focusing force just balances th e space charge forces. The limit to the current due to transverse focusing can be found s by solving the beam envelope equations using the 'smooth approximation', giving
I, =~R 1o/~3y'3'~°°°~ =,[1 12
(~r/~,) z ]
(3)
The hollow beam transport facility, shown in Figure 3, is designed to work in conjunction with the GSI high-current ion source CORD1S 4. Although not originally intended to produce hollow beams, the large diameter of CORDIS makes it possible to extract hollow beams of up to 35 mm dia. Extrapolating the results obtained from operation with multi-aperture extraction indicates that sufficient current to test the transport system can be extracted with three slits formed in a ring 35 mm in dia and 3 mm wide. This extraction geometry was also checked with the GSI version of the AXCEL 8 computer code, a particle simulation program that incorporates space charge and models the plasma boundary in the ion source. The simulation of the beam forming process is shown in Figure 4. The periodic transport section requires a hollow beam of 125 mm dia. A matching section expands the hollow beam from the ion source out to this diameter by means of an electrostatic coaxial doublet. The matching section must also match the beam emittance to the acceptance of the periodic channel. A ring einzel lens immediately after the coaxial doublet assists in adjusting the tilt of the beam emittance ellipse to optimize the matching. The trajectories of the particles in this section were also computed under space charge conditions and the results are shown in Figure 5. The iteration procedure used to incorporate space charge into the computation is, however, less successful in a system that deflects and focuses the beam. In a system such as the extraction region of an ion source, the particles follow near straight-line paths and the space charge only alters the divergence of the rays. In simulating the matching section, however, the space charge matrix produced in the first iteration alters the path of the rays as well as their divergence, creating a false space charge matrix for t h e second iteration. The iteration technique only converges for relatively weak space charge conditions in such cases. At the other end of the transport section, a second coaxial doublet acts as a final focus lens. The coaxial lens also behaves in this instance as a cylindrical electrostatic septum, recombining the hollow beam into an axial beam. Beam emittance measurements can thus be made in the end diagnostic chamber, on both the large diameter, hollow beam and on the recombined, axial beam. The periodic focusing channel is of modular construction and uses a single, long metal tube as a common inner electrode for the lenses. The lens outer cylinders are sandwiched together, with insulating rings between each segment. The lens cylinders also
÷
r..r~, ~ .
N
tl
Jf!j
4
0.6m MA'TCHtNt~ SECTtON
CONVERGING COAXIALLENS
.4
llm CELLS
l/ 3.8m I
INNER ELECTR00E
ivERC~i
/,.3m BEAMDIAGNOSTICS
t,.07m 4
SEP[Ut.t
LENSEI~TTANCEHEASU~ING SYSTEM
FINALFO(US LENS ANO SEPTUM
NEGATIVE CONVERC.4Nfi LENS
GROUND ELECTROOE
POSJTIVE
12 FOCUS~-OEFOCUSING
INNER ELECTRO0~ SUPPORT
RINGFOCUSLENS
Fi@re 3. The hollow bedm test stand at GSI accepts a 35 mm dia hollow beam from a high-current ion source for heavy ions. The matching ,~cction expands this beam to 125 mm dia for transport in the periodic focusing section consisting o1"12 coaxial cells. A final focus doublet allows the hollow beam to be focused into a full beam for emittance measurements.
tON SOUREE
~'
J
DIVERGING COAXIALLENS
FARAOAY CUP
=_.
=3
=[
o m O
o_.
;3,
3
g
¢D
e-
~5'
:3"
~>
P Krejcik and R Keller: A high-current beam transport facility for hollow beams
current focusing phase advance per cell of 1 rad and a corresponding sectional radial acceptance of 5.85 × 10 -4 rad m. These figures are for very conservative operation of the channel since the corresponding maximum field strength in the channel is only l0 s V m-1. The space-charge limited current of the channel is dependent on the type of particle transported. For example, from equation (3) the current limit for a 50 keV beam of4°Ar + is 0.078 × (a0oo)2, so that for the above operating conditions l,(4°Ar + ) = 78 m A and for protons under the same conditions I,(IH + ) = 4 8 0 rnA.
E E
The current limit is also a function of the particle energy and increases in proportion to W 3/2.The current limits calculated here are not the theoretical maximums for the channel because of the relatively low field strengths. On the other hand, the insulator design in our test facility does not permit higher voltages to be used. The beam measurements to be made with the facility are rather to check the validity of equations (1) and (3).
4. Beam measurements
Figure 4. The hollow beam extraction geometry for the ion source as modelled in the space charge calculations of the computer code AXCEL-GSl.
form the walls of the vacuum chamber, so no HV leadthroughs are needed. The main parameters of the periodic focusing channel are listed below. No. of cells: 12. Total length: 2.75 m. Length of each lens cylinder, L:60 mm. Distance between lens centres, D: 113 ram. Lens outer radius: 75 mm. Lens inner radius: 52 ram. Zero-current focusing phase advance per cell, aoo 0: 2.3 x (Vff W) rad. Sectional radial acceptance, co,: 5.85 x 10-4x Croo0 rad m. From these values it can be seen that for particles of energy W = 50 keV, lens voltages of approximately 22 kV will give a zero14
First tests with the hollow beam extraction system showed the need for some improvements in cooling of the electrodes and alignment of extraction apertures. The original extraction system using nine small apertures arranged in a ring has been replaced by precision circular slits machined on a numerically controlled milling machine. The electrodes are also now mounted on copper tubes for better heat dissipation. The alignment of the inner electrode in the matching section was also found to be critical in the region immediately after the ion source where the beam diameter is small. Once the beam has been expanded to a large diameter, radial displacements produce only a small relative error in the alignment. In an electrostatic focusing system, the electrons produced by the beam in the background gas, or due to stray beam colliding with the walls, are removed from the system through the positive lenses. In the matching section this caused considerable heat dissipation in the second lens. This requires that the second lens is water cooled. An additional clearing electrode has also been added between the ion source and the matching section to remove some of the electrons at a lower potential. Provision has also been made to raise the potential of the inner electrode along the entire length of the structure by a few hundred volts, to draw off electrons from the system. Beam measurements at the end of the matching section have been made both with foil targets and a Farraday cup. The beam striking the foil target causes it to incandesce and is a quick diagnostic technique for checking the symmetry of the beam and hence the alignment of the system. The ring image of the beam on the target is well defined so it is possible to measure the beam diameter and width as a function of the voltage on the lens doublet. This was done at two different positions of the target after the matching section. A graph of lens voltage vs beam diameter at the two different locations, as in Figure 6, allows the conditions for producing a parallel beam of the necessary diameter to be found. In a separate measurement, beams of 25 mA of 34 keV 4°Ar÷ were recorded in a large diameter Faraday cup at the end of the
P Kteicik and R Keller. A high-current beam transport facility for hollow beams
(m) ,OO
,
C,,'~ C
C'=~,:
,3 ,3~
,
C~C:
C:5C'
Z=::~
J-'~C
0
-d
Ol~lO A
o.E
c' v-i. O w o
-o,
(clearing)
matchingdoub[et einze[lens
FO DO .ceils
Figure 5. Ray tracing in the matching section of the test facility simulated under weak space charge conditions.
obvious how to optimize the matching section with the ion source, to maximize the current, and at the same time produce the correct matching conditions for the periodic focusing section. It is hoped to find a better optimizing procedure during the next stage of measurements, with the beam transported in the periodic focusing section.
/
105
5. Acknowledgements The authors wish to thank P Sp~idtke for his assistance with the A X C E L - G S I code. Uu (kV)= -3 0
o
-~.
-5
-6
-7 -B-9
,b
I
References --
POSITIVE LENS VOLTAGE UL2 (KV)
Figure 6. Measuring the beam diameter at two locations after the matching section ( x :82.5 cm from source; O : 116 cm from source) as a function of doublet voltages allows conditions for a parallel beam (dashed line) to be found. Beam energy is 33 keV in this case. matching section. The dependence of the matching conditions on space charge is such that in operation it is not immediately
Ip Krejcik, Proc Syrup on Accelerator Aspects o f Heavy Ion Fusion, Darmstadt, GSI 82-8, pp 255-274 (1982). 2p Krejcik, Proc 1983 Particle Accelerator Conf Santa Fe, 21-23 March, IEEE Trans Nucl Sci NS-30, 3168 (1983). n p Krejcik, J C Kelly and R L Dalglish, Nucl lnstrum Meth 168, 217 (1980). 4 R Keller, F N6hmayer, P Sp~idtke and M H Sch6ncnberg, Vacuum 34, 31 (1984). ~P Krejcik and R W M/filer, CiS! Internal Report. to be published. 6M Reiser, Particle Accelerators 8, 167 (1978). vI Hoffman, L J Laslett, L Smith and I Habcr, LBL Report-1492! Particle Accelerators, to be published. sp Sp~idtke, GSI Internal Report, to be published.
15
0042-207X/84S3.00+.O0 Pergamon Press Ltd
A high-current beam transport facility for hollow beams P Krejcik, Kernforschungsanlage, JiJlich, W Germany and R Keller, Gesellschaft fdr Schwerionenforschung, Darmstadt, W Germany
A test experiment is reported in which a hollow beam is transported using a focusing system based on electrostatic coaxial lenses. The principle of this focusing system is described and design formulae given for the space charge limited current, which predict higher beam currents than with conventional focusing systems. Experimental beam measurements are presented together with results of computed space charge simulation in the beam, and matching conditions for the beam are described.
i. Introduction At low energies, beam brightness is generally limited through space-charge effects. High currents can be transported if the beam is fully space-charge neutralized, but this is only possible in the absence of electric fields. In the acceleration process, therefore, space charge forces in the beam will limit the current. The upper limit to the current is determined by the strength of the focusing forces available to balance the space charge forces. At low energies there are problems in providing strong focusing. The low particle velocities, particularly for heavy ions, reduce the efficiency of magnetic quadrupoles, and electric quadrupoles are also limited in strength by the aperture to length requirements and by the maximum electric field strength set by sparking. A new system I has been proposed that uses electrostatic coaxial cylinder lenses to provide strong focusing for hollow beams. In this system the space charge density is reduced by distributing ihe beam over a large annular aperture, but at the same time the focusing strength is maintained by the radial electric field between the inner and outer lens cylinders. In this way, the space-charge limited current of the transport system is raised beyond that of conventional, axial transport systems, as will be further described below. This feature of the hollow beam system makes it attractivefor consideration as a high-brightnessinjectorfor large,high-energy machines such as the spallationneutron source accelerator,and a possible future heavy-ion driver accelerator for inertialconfinement fusion. This is particularly so since the coaxial focusing principle for hollow beams can also be extended to a continuous focusing radio frequency linearaccelerator2.This rfstructure can bunch and acceleratea beam directlyfrom the ion source,thereby avoiding difficultieswith high-voltage dc accelerators for high currents. The favourable beam properties,as well as the simple construction of coaxial focusing elements, lend themselves also to more general applications of low-energy ion beam technology.
The ability to correct spherical and chromatic aberrations in finalfocus coaxial lenses 3 further extends the applications to microbeam technology. A hollow beam facility has been commissioned at GSI to test the beam transport characteristics of the coaxial focusing system. It accepts a beam of up to 50 keV of heavy ions from the highcurrent ion source CORDIS 4 and transports it through a periodic focusing system to a beam diagnostics chamber where beam emittance measurements can be made. The principle of the periodic focusing system is discussed in the next section, followed by a description of the facility. Beam measurements that have so far been made are compared to computer simulations of the beam-forming system.
2. Strong focusing of hollow beams with coaxial lenses The radial electric field between coaxial cylinders acts transversely on a hollow beam, deflecting it either toward or away from the axis depending on the sign of the applied field. The 1/r dependence of the electric field does not cause linear focusing about the lens axis. However, in a periodic system made up of converging and diverging lenses, as shown in Figure 1, the focusing is linear about the equilibrium path taken by the beam. This linear focusing gradient acts across the radial width, or thickness, of the hollow beam. The focusing field seen by the beam is diverging when the beam is deflected toward the axis and converging during deflection away from this axis. The focusing action is also characterized by the motion, in the r - r ' plane, of the panicles' co-ordinates at the end of each focusing period. In the r - r ' plane the particles trace out eigenellipses centred on a fixed point corresponding to the equilibrium trajectory, as shown in Figure 2. The sectional radial emittance, t,, of the beam can be represented by the area of such an ellipse, displaced from the origin, in the r - r ' plane. 11
A high-current beam transport facility for hollow beams
P Krejcik and R Keller:
eq~iibrium trajectory \.
for particles of velocity tic and where
÷
Io = 4neomoca/q" 3.1 x I 0 ~ A / Z [ a m p e r e s ] .
Figure i. Strong, alternating-gradient focusing for hollow beams is provided by the radial electric field between coaxial cylinders. The trajectories shown are for a periodically focused beam in a defocusing focusing cell.
eigen-ettipse
.
This current limit is a factor 2R/b greater than that given by Reiser 6 for periodic focusing of conventional, axial beams, where the sectional radial emittance and acceptance in equation (3) are replaced by their corresponding quantities in the axial beam case. The factor 2Rib does not, however, imply that the current limit can be increased indefinitely by making the beam large in radius and narrow in section since the focusing phase advance given by equation (1) also decreases with R. On the other hand, ooo0 cannot exceed the 2n stop-band, and for beam stability reasons 7 it should even be kept below n/2. Taking this additional boundary condition into account, the coaxial system is able to transport considerably more current than axial systems, as we shall see in the specific design example in the next section.
3. The hollow beam test stand
",,--
fixed poin~" / ~ ' ~ I I f I r~dius r
R
Figure 2. The r - r' plane of the hollow beam phase space. The fixed point corresponds to the equilibrium orbit of a periodically focused beam. Adjacent trajectories tracc out ellipses as they pass through consecutive cells. The area of the large possible ellipse is the sectional radial acceptance, =,, of the structure. The strength of the focusing is given by the normalized angular advance the particle makes around the eigen-ellipse after each focusing period. This focusing phase advance per cell can be readily calculated to first order, from a knowledge of the electric field strength at the average radius R = (% + r3/2 of the beam. For a particle potential W and a lens potential V~ this is given by
V~LD
(1)
aooo = 2 w R 2 In ro/ri where lenses of length L have spacing D between their centres; r o and r~ are the outer and inner lens cylinder radii and b = ( t o - r3/2. A point to note is that the potential on the diverging and converging lenses cannot have the same magnitude if the equilibrium trajectory has an average radius halfway between the inner and outer cylinders. This is due to the reduction in the electric field in the diverging lens where the trajectory radius is maximum. The sectional radial acceptance, ~,, of a focusing cell of length S is given by the area of the largest possible eigen-ellipse in the r - r' plane and is
[2)
=, = aooob2/S.
The space charge limited current in a transport channel is reached when the restoring focusing force just balances th e space charge forces. The limit to the current due to transverse focusing can be found s by solving the beam envelope equations using the 'smooth approximation', giving
I, =~R 1o/~3y'3'~°°°~ =,[1 12
(~r/~,) z ]
(3)
The hollow beam transport facility, shown in Figure 3, is designed to work in conjunction with the GSI high-current ion source CORD1S 4. Although not originally intended to produce hollow beams, the large diameter of CORDIS makes it possible to extract hollow beams of up to 35 mm dia. Extrapolating the results obtained from operation with multi-aperture extraction indicates that sufficient current to test the transport system can be extracted with three slits formed in a ring 35 mm in dia and 3 mm wide. This extraction geometry was also checked with the GSI version of the AXCEL 8 computer code, a particle simulation program that incorporates space charge and models the plasma boundary in the ion source. The simulation of the beam forming process is shown in Figure 4. The periodic transport section requires a hollow beam of 125 mm dia. A matching section expands the hollow beam from the ion source out to this diameter by means of an electrostatic coaxial doublet. The matching section must also match the beam emittance to the acceptance of the periodic channel. A ring einzel lens immediately after the coaxial doublet assists in adjusting the tilt of the beam emittance ellipse to optimize the matching. The trajectories of the particles in this section were also computed under space charge conditions and the results are shown in Figure 5. The iteration procedure used to incorporate space charge into the computation is, however, less successful in a system that deflects and focuses the beam. In a system such as the extraction region of an ion source, the particles follow near straight-line paths and the space charge only alters the divergence of the rays. In simulating the matching section, however, the space charge matrix produced in the first iteration alters the path of the rays as well as their divergence, creating a false space charge matrix for t h e second iteration. The iteration technique only converges for relatively weak space charge conditions in such cases. At the other end of the transport section, a second coaxial doublet acts as a final focus lens. The coaxial lens also behaves in this instance as a cylindrical electrostatic septum, recombining the hollow beam into an axial beam. Beam emittance measurements can thus be made in the end diagnostic chamber, on both the large diameter, hollow beam and on the recombined, axial beam. The periodic focusing channel is of modular construction and uses a single, long metal tube as a common inner electrode for the lenses. The lens outer cylinders are sandwiched together, with insulating rings between each segment. The lens cylinders also
÷
r..r~, ~ .
N
tl
Jf!j
4
0.6m MA'TCHtNt~ SECTtON
CONVERGING COAXIALLENS
.4
llm CELLS
l/ 3.8m I
INNER ELECTR00E
ivERC~i
/,.3m BEAMDIAGNOSTICS
t,.07m 4
SEP[Ut.t
LENSEI~TTANCEHEASU~ING SYSTEM
FINALFO(US LENS ANO SEPTUM
NEGATIVE CONVERC.4Nfi LENS
GROUND ELECTROOE
POSJTIVE
12 FOCUS~-OEFOCUSING
INNER ELECTRO0~ SUPPORT
RINGFOCUSLENS
Fi@re 3. The hollow bedm test stand at GSI accepts a 35 mm dia hollow beam from a high-current ion source for heavy ions. The matching ,~cction expands this beam to 125 mm dia for transport in the periodic focusing section consisting o1"12 coaxial cells. A final focus doublet allows the hollow beam to be focused into a full beam for emittance measurements.
tON SOUREE
~'
J
DIVERGING COAXIALLENS
FARAOAY CUP
=_.
=3
=[
o m O
o_.
;3,
3
g
¢D
e-
~5'
:3"
~>
P Krejcik and R Keller: A high-current beam transport facility for hollow beams
current focusing phase advance per cell of 1 rad and a corresponding sectional radial acceptance of 5.85 × 10 -4 rad m. These figures are for very conservative operation of the channel since the corresponding maximum field strength in the channel is only l0 s V m-1. The space-charge limited current of the channel is dependent on the type of particle transported. For example, from equation (3) the current limit for a 50 keV beam of4°Ar + is 0.078 × (a0oo)2, so that for the above operating conditions l,(4°Ar + ) = 78 m A and for protons under the same conditions I,(IH + ) = 4 8 0 rnA.
E E
The current limit is also a function of the particle energy and increases in proportion to W 3/2.The current limits calculated here are not the theoretical maximums for the channel because of the relatively low field strengths. On the other hand, the insulator design in our test facility does not permit higher voltages to be used. The beam measurements to be made with the facility are rather to check the validity of equations (1) and (3).
4. Beam measurements
Figure 4. The hollow beam extraction geometry for the ion source as modelled in the space charge calculations of the computer code AXCEL-GSl.
form the walls of the vacuum chamber, so no HV leadthroughs are needed. The main parameters of the periodic focusing channel are listed below. No. of cells: 12. Total length: 2.75 m. Length of each lens cylinder, L:60 mm. Distance between lens centres, D: 113 ram. Lens outer radius: 75 mm. Lens inner radius: 52 ram. Zero-current focusing phase advance per cell, aoo 0: 2.3 x (Vff W) rad. Sectional radial acceptance, co,: 5.85 x 10-4x Croo0 rad m. From these values it can be seen that for particles of energy W = 50 keV, lens voltages of approximately 22 kV will give a zero14
First tests with the hollow beam extraction system showed the need for some improvements in cooling of the electrodes and alignment of extraction apertures. The original extraction system using nine small apertures arranged in a ring has been replaced by precision circular slits machined on a numerically controlled milling machine. The electrodes are also now mounted on copper tubes for better heat dissipation. The alignment of the inner electrode in the matching section was also found to be critical in the region immediately after the ion source where the beam diameter is small. Once the beam has been expanded to a large diameter, radial displacements produce only a small relative error in the alignment. In an electrostatic focusing system, the electrons produced by the beam in the background gas, or due to stray beam colliding with the walls, are removed from the system through the positive lenses. In the matching section this caused considerable heat dissipation in the second lens. This requires that the second lens is water cooled. An additional clearing electrode has also been added between the ion source and the matching section to remove some of the electrons at a lower potential. Provision has also been made to raise the potential of the inner electrode along the entire length of the structure by a few hundred volts, to draw off electrons from the system. Beam measurements at the end of the matching section have been made both with foil targets and a Farraday cup. The beam striking the foil target causes it to incandesce and is a quick diagnostic technique for checking the symmetry of the beam and hence the alignment of the system. The ring image of the beam on the target is well defined so it is possible to measure the beam diameter and width as a function of the voltage on the lens doublet. This was done at two different positions of the target after the matching section. A graph of lens voltage vs beam diameter at the two different locations, as in Figure 6, allows the conditions for producing a parallel beam of the necessary diameter to be found. In a separate measurement, beams of 25 mA of 34 keV 4°Ar÷ were recorded in a large diameter Faraday cup at the end of the
P Kteicik and R Keller. A high-current beam transport facility for hollow beams
(m) ,OO
,
C,,'~ C
C'=~,:
,3 ,3~
,
C~C:
C:5C'
Z=::~
J-'~C
0
-d
Ol~lO A
o.E
c' v-i. O w o
-o,
(clearing)
matchingdoub[et einze[lens
FO DO .ceils
Figure 5. Ray tracing in the matching section of the test facility simulated under weak space charge conditions.
obvious how to optimize the matching section with the ion source, to maximize the current, and at the same time produce the correct matching conditions for the periodic focusing section. It is hoped to find a better optimizing procedure during the next stage of measurements, with the beam transported in the periodic focusing section.
/
105
5. Acknowledgements The authors wish to thank P Sp~idtke for his assistance with the A X C E L - G S I code. Uu (kV)= -3 0
o
-~.
-5
-6
-7 -B-9
,b
I
References --
POSITIVE LENS VOLTAGE UL2 (KV)
Figure 6. Measuring the beam diameter at two locations after the matching section ( x :82.5 cm from source; O : 116 cm from source) as a function of doublet voltages allows conditions for a parallel beam (dashed line) to be found. Beam energy is 33 keV in this case. matching section. The dependence of the matching conditions on space charge is such that in operation it is not immediately
Ip Krejcik, Proc Syrup on Accelerator Aspects o f Heavy Ion Fusion, Darmstadt, GSI 82-8, pp 255-274 (1982). 2p Krejcik, Proc 1983 Particle Accelerator Conf Santa Fe, 21-23 March, IEEE Trans Nucl Sci NS-30, 3168 (1983). n p Krejcik, J C Kelly and R L Dalglish, Nucl lnstrum Meth 168, 217 (1980). 4 R Keller, F N6hmayer, P Sp~idtke and M H Sch6ncnberg, Vacuum 34, 31 (1984). ~P Krejcik and R W M/filer, CiS! Internal Report. to be published. 6M Reiser, Particle Accelerators 8, 167 (1978). vI Hoffman, L J Laslett, L Smith and I Habcr, LBL Report-1492! Particle Accelerators, to be published. sp Sp~idtke, GSI Internal Report, to be published.
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