Eddy current focusing solenoid
Martin Paraliev
n, Christopher Gough, Sladjana Ivkovic, Lukas Stingelin
Large Research Facilities, WSLA-014, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
a r t i c l e i n f o
Article history:
Received 26 October 2010 Received in revised form 4 January 2011
Accepted 18 January 2011 Available online 4 February 2011 Keywords:
Pulsed solenoid Focusing magnet Eddy currents
a b s t r a c t
A novel eddy current based focusing solenoid concept was developed, in which the eddy currents are used to generate the main focusing field rather than controlling the field distribution. In general, an air- core solenoid coil with a small number of turns gives a solenoid field that is contaminated with unwanted dipole and higher order transverse fields. In concept this problem can be avoided by using filamentary ring with induced current. The concept was proved using numerical simulation and physical models. A real eddy current focusing solenoid was designed and constructed with a six-turn solenoid as excitation coil and a15 mm diameter filamentary metal ring as secondary. For practical application, the secondary ring had to be implemented as a short hollow cylinder. Slicing this cylinder into segments suppresses transverse fields in the same way as for a series of filamentary rings. The developed solenoid field can reach over 300 mT. The mechanical and electrical design, numerical field simulations and measurements with an electron beam are presented.
&2011 Elsevier B.V. All rights reserved.
1. Introduction
For the SwissFEL project, a low emittance electron gun (LEG) test stand[1]was built and commissioned[2]. This test stand is used to study and optimize generation and transport of low emittance electron beams. After initial acceleration in a pulsed diode, the electron bunch is focused to match the electron beam envelope to the following RF accelerating structure[3,4]. Pulsed magnetic focusing based on a novel eddy current concept was adopted for this focusing to give compact design with good magnetic screening of cathode. This scheme reduces complexity of the solenoid in-vacuum components and it does not require field cancellation coil as this is necessary for a DC design[5].
2. Eddy current concept and transverse field suppression scheme
For a solenoid coil without magnetic core, a small number of turns means that the solenoid field is contaminated with unwanted dipole and higher order transverse fields due to non- negligible magnetic field contribution of the solenoid terminals.
In concept this problem can be avoided by using filamentary ring with induced current. In Fig. 1, the filamentary metal ring is aligned with the desired axis of the particle beam. The excitation coil (primary) is magnetically coupled to the ring and it is used to
induce the eddy currents. Symmetry and alignment requirements for the excitation coil are relaxed because the useful magnetic field is generated (sustained) by the eddy currents that flow in a symmetric planar filamentary ring.
The magnetic field in the working volume is generated by currentIexflowing through the excitation coil.
Eddy currents in the ring create an opposing magnetic field that fights the flux change. Due to the resistive losses in the ring, after some hundred microseconds, the induced eddy currents have reduced to a low value and static fieldBexis established. At this time, the excitation current Iex is turned off rapidly. The existing field is sustained by the eddy currentIeddyin the ring.
Because the eddy current is restricted to flow in a plane perpen- dicular to ring axis it sustains only the longitudinal field compo- nent. Even if the direction of excitation field Bex has not been perfectly aligned to the beam axis or has had asymmetries, the electron beam sees an aligned and symmetric focusing fieldBf.
Practical implementation and alignment of filamentary conduct- ing ring are difficult. A machined hollow cylinder with tight mechanical tolerances could be well aligned to the mechanical axis of the machine. Unlike a filamentary ring, the cylinder would permit unwanted longitudinal eddy current components and the field transverse structure of the excitation coil will be kept. To solve this, the cylinder was sliced into a series of rings to suppress longitudinal currents. To explore this scheme, a physical model shown inFig. 2 was built and characterized. A rotatable excitation coil was used to generate magnetic field with defined direction. A set of differently segmented secondary cylinders was prepared and tested.
‘‘Stretched wire’’ technique was used to measure the transverse magnetic field and to evaluate the transverse field suppression Contents lists available atScienceDirect
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Nuclear Instruments and Methods in Physics Research A
0168-9002/$ - see front matter&2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.nima.2011.01.081
nCorresponding author. Tel.: +41 56 310 5151; fax: + 41 56 310 4528.
E-mail address:martin.paraliev@psi.ch (M. Paraliev).
capabilities versus segmentation. This technique is widely used to measure fields and field integrals of different static magnetic field sources [6,7]. To generate changing magnetic flux longitudinally positioned stretched wire is movable or vibrating. It crosses mag- netic flux lines and an electric signal is generated at the two ends of the wire according to Faraday’s law. In case of pulsed magnetic field measurements a mechanical movement is not necessary. The stretched wire has to be transversely displaced (with respect to the solenoid axis) in order to become sensitive to field rotation
around the displacement direction. The excitation coil was deliber- ately rotated 201in order to generate large transverse field compo- nent (36% of the field on axis). Large rotation angle (201) was chosen in order to make the transverse field component large and to increase measurement accuracy. Table 1 summarizes measured longitudinal and transverse magnetic field 12
m
s after excitation current is stopped for different segmentation of the cylinder. The resultant angular misalignment of the focusing field and transverse field components suppression factor are shown there as well.The same layout was simulated, using 3D numeric electro- magnetic solvers (ANSYSs [8] and CST EM STUDIOs [9]). Both simulations agree very well and show reduction in the transverse field component with increase in the number of slices.
Figs. 3 and 4show simulated and measured resultant focusing field angle with respect to the cylinder axis for different segmen- tations of the cylinder. Vertical dashed line indicates the moment when excitation current is switched off and the solid one indicates the field measurement time (forTable 1). Near the end of excitation phase, initiated eddy currents fade off and all graphs converge to 201(static magnetic field at 201angle is established).
After excitation current is switched off, the eddy current reap- pears, sustaining the established magnetic field. Currents that flow in planes not perpendicular to the cylinder axis tend to decay faster because of the anisotropic cylinder conductivity, due to its segmentation. The more segmented the hollow cylinder is the faster the magnetic field angle approaches zero (aligns with the hollow cylinder axis). If the electron bunch passes many micro- seconds after the excitation current is stopped, it sees focusing Fig. 1.First, excitation currentIexestablishes static magnetic fieldBex. After the
current Iex is turned off, the remaining eddy current Ieddy, flowing in the filamentary metal ring, gives symmetric solenoid fieldBf, well aligned with the electron beam axis.
Fig. 2.Layout of physical model (cross-section): (a) not segmented hollow cylinder, (b) segmented hollow cylinder (4 segments) and (c) segmented hollow cylinder (8 segments).
Table 1
Simulated and measured values of longitudinal and transversal magnetic field components versus segmentation of the ring in the physical model.
Value and configuration ANSISs CST EM STUDIOs Measured
Main field (mT) Non-segmented 9.81 10.32 10.0670.16
4 segments 10.01 10.10 9.8370.15
8 segments 9.84 9.91 9.9270.16
Transverse field (mT) Non-segmented 2.76 2.90 1.6570.03
4 segments 0.11 0.13 0.2970.03
8 segments 0.06 0.08 0.0870.03
Angular misalignment (deg.) Non-segmented 15.71 15.70 9.3370.30
4 segments 0.62 0.74 1.6870.19
8 segments 0.34 0.46 0.4870.17
Suppression factor (dB) Non-segmented 1.12 1.12 3.4570.14
4 segments 15.24 14.51 10.9570.47
8 segments 17.84 16.54 16.4271.34
magnetic field, well aligned with the hollow cylinder axis. At the beginning and at the end of the measured curves the angular information becomes noisy and looses relevance due to the fact that field components approach zero.
3. Construction
Fig. 5shows a cross-section of the built solenoid inside the vacuum chamber. The excitation coil conductor b(copper tube 32 mm) is brazed in a spiral channel machined into isolating ceramic base c and it is water cooled. The complete pulsed solenoid is 80 mm long with a clear beam diameter inside the cylinder of 10 mm. Precision machining of the focusing cylindera (segmented hollow cylinder) and the ceramic base (after brazing of the end flanges g and h) ensures alignment. Three precisely machined contact surfaces on the ceramic base flangegare used to align the solenoid with RF cavityf. On both sides, the focusing cylinder extends with thin wall tube to keep beam impedance unchanged. One side of thin wall extension ends with a thread and alignment shoulders and forms the interface to the anodee.
Fig. 6shows in detail the cross-section of the focusing cylinder. In practical implementation, the filamentary metal ring should be aligned on the electron beam axis with an error below 50
m
m and a direction error below 1 mrad. The angular error cannot be easily controlled unless the ring is rather more a cylinder in shape.The excitation current in the primary has to flow several times longer than the cylinder time constant. If high conductivity metal, such as copper, is used, the excitation current needs to flow longer, giving unacceptable power dissipation.
If low conductivity metal is used, the eddy currents will fade off faster and the electron beam will see lower focusing field.
There for middle range conductivity metal was chosen (stainless steel, type 316L
r
¼7.4107Om). The cylinder is 24 mm long and its outer diameter is 17 mm (machined with 10m
m toler- ance). For this choice of metal the electrical time constant of the cylinder is about 10m
s.4. Thermal management
Since the pulse solenoid is in vacuum a thermal path should be provided to conduct the heat dissipated in the excitation (pri- mary) coil and the focusing cylinder. Single pulse dissipated energy in the primary and in the focusing cylinder are, respec- tively, 2.21 and 0.355 J (221 and 35.5 W for 100 Hz operation).
The primary is made up of Cu tube and temperature stabilized water cooling (1 l/s) is provided. The resultant heat sink thermal resistance is 0.0141C/W. If the heat flowing through the ceramic base end flanges is neglected, the total amount of heat (generated in the primary and in the focusing cylinder) is dissipated through the water flowing through the primary and its average tempera- ture will rise with 3.61C.
The heat transfer for the focusing cylinder occurs through the ceramic base (alumina). The primary is brazed to the ceramics to ensure good thermal contact. The thermal resistance through the Fig. 3.Simulated values, showing field angle with respect to the cylinder axis for
different cylinder segmentation. Upper traces – field direction; lower – excitation current.
Fig. 4.Measured field angle with respect to the cylinder axis for different focusing hollow cylinder segmentations. Upper traces – field direction, lower – excitation current. The larger angles that occur more than 20ms after the turn-off are not relevant because the field magnitude approaches zero and measurement errors become large.
Fig. 5.Cross-section of the pulsed solenoid region: (a) focusing cylinder, (b) water cooled excitation coil, (c) ceramic base, (d) anode plate, (e) anode, (f) RF cavity, (g and h) ceramic base flanges.
Fig. 6.Cross-section of the focusing hollow cylinder.
ceramics is 0.191C/W. Assuming good contact between ceramic base and the focusing cylinder (precision machined surfaces) the average temperature rise of the cylinder above the cooling water temperature will be 6.71C. The thermal capacity of the active part of the focusing cylinder is 11.9 J/1C and the pulsed overheating will be 0.031C and it could be neglected.
The switch dissipates the rest of inductively stored energy in the system, which at full magnet current is 10.6 J per pulse or 1060 W at 100 Hz operation. The transistor switches are mounted on three forced air cooled heat sinks with thermal resistance 0.11C/W each. At full magnet current the heat sink temperature will rise with 351C above the ambient air temperature.
5. Solenoid driver
A simplified equivalent circuit of the pulsed solenoid together with its driving circuit is shown inFig. 7. ComponentsV1,I1and D1represent a charging power supply with current limit of 5 A.
Inductor L1 and capacitor C2 represent stray inductance and parasitic capacitance of the switch and connecting wires.
The main capacitorC1is charged through the diodeD3. When the switch S1 closes the storage capacitor C1 is discharged through the excitation coilL2(R2represents its DC resistance).
Once the desired field is established (about 30% higher than the required focusing field) the switch opens and the excitation currentIexstops. The magnetic field is sustained by eddy current Ieddyflowing through focusing cylinder represented byL3andR3.
The voltage across the switch (Usw) rises rapidly due to stored magnetic energy in the stray and uncoupled inductances and this energy is dissipated in the switch. UsingV2andD2the voltage is clamped to a fixed value to protect the switch from overvoltage.
Excitation current (Iex) ramps linearly down to zero and the time needed to reach zero depends on its amplitude value. ResistorR1 damps the unwanted oscillation of parasitically formed resonator
L1–C2after turn-off transient.Fig. 8shows the typical voltage and current waveforms in the circuit.
6. Switch
To ensure a fast current interruption, the switch has to turn-off quickly under heavy inductive load. An IGBT with 4 kV 40 A ratings (IXEL40N400[10]) was chosen as the switching element.
Each transistor in the switch has a local feedback to prevent complete turn-off if the voltage across the transistor exceeds 3.8 kV. The total inductance in the circuit Ltot is about 4
m
H.Assuming constant voltage over the switchUsw, the transient time Dtuntil the excitation currentIexreaches zero is given by Dt¼Ltot
Iex
Usw
: ð1Þ
In order to reduce the complexity of the on–off switch there was preference to avoid multi-row topology, so accepting max- imum voltage over the switch of 3.8 kV. Maximum current was chosen to be 2.5 kA in order to give the required 260 mT on axis, with some safety margin. From Eq. (1), the linear turn-off transient will last up to 2.6
m
s. During turn-off, the peak power dissipation in the switch is 9.5 MW. The switch consists of eighteen transistors (max pulsed current 170 A) in parallel. To drive the gate of each transistor, a 0.5 A isolated gate driver IC (FOD3181[11]) was used. Small series inductances (0.5m
H) and transistor on-resistance are used to ensure current sharing. The average power dissipated at full current and repetition rate of 100 Hz is about 70 W per transistor.7. Jitter, stability and head–tail effects
Pulse-to-pulse magnetic field amplitude jitter has two main components: jitter due to storage capacitor charging voltage fluctuations and translated time-to-amplitude jitter due to chan- ging magnetic field of the solenoid. Since the solenoid magnetic field is directly proportional to the pulser charging voltage, the first component of the relative field amplitude jitterJAis equal to the charging power supply relative ripple stability, which in our case is 1104rms.
The second relative amplitude jitter component is due to the fact that the field is not static but decays exponentially and the timing jitter translates in amplitude jitter. Eq. (2) describes the decay of the magnetic field in time B(t) after excitation current turn-off:
BðtÞ ¼Bmaxet=t: ð2Þ
whereBmaxis the magnetic field established by the excitation coil, tis time and
t
is the focusing cylinder time constant. Magnetic field sensitivity to timeðdB=dtÞis given by the derivative of Eq. (2):dB
dt ¼ Bmax
t
et=t ð3Þ
For the relative time induced jitter estimation the largest absolute derivative value is considered (att¼0).
dB dt
t¼0¼ Bmax
t
: ð4ÞMaximum time induced relative amplitude sensitivity ST is given by
ST¼dB dt t¼0 1
Bð0Þ¼ 1
t
ð5ÞFig. 7.Equivalent circuit of pulsed solenoid and its driver.
Fig. 8.Typical simulated waveforms: voltage over the switch (Usw).
Eq. (6) gives estimated relative amplitude jitter due to timing JTfor measured time jitter of the pulser turn-offJTrigg¼2 ns rms:
JT¼jSTjJTrigg¼1:9104rms ð6Þ
The two jitter sources are uncorrelated and the total relative amplitude shot-to-shot jitterJtotis given by
Jtot¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi JA2þJ2T q
¼2:17104rms ð7Þ
Eq. (5) could be used to estimate the head–tail effects on the electron beam focusing. For this machine photo-emitted electron bunch is maximum 30 ps long. The relative magnetic field head–
tail change is maximum 2.9 ppm. For such electron bunch length this effect could be neglected.
Eq. (8) defines long term relative drift dIex of the maximum value of excitation current Iex. Five hundred samples moving average (200 s average) is used to remove shot-to-shot jitter:
dIex¼/IexS500/IexS
/IexS ð8Þ
where/IexS500is moving average of 500 samples and/IexSis the average of the whole series.
Fig. 9 shows long term relative drift of the system for more than 2 h operation (excitation solenoid current is set to 1000 A, rep. rate 10 Hz, every 4th pulse is recorded). For the shown period dIexis below 2 ppt and it satisfies current machine requirements (better than 1%).
Measured relative rms shot-to-shot excitation current ampli- tude jitter of a series 1000 pulses is 1.71104(same conditions as for the above measurement, average of 10 consequent series).
It agrees well with the expected value.
8. Pulsed versus DC operation
For the particular electron gun application there are several important points that justify the choice of increased complexity of a pulsed solution.
Magnetic field screening. For low emittance electron beam emission the magnetic field on the cathode should be zero. If DC solenoid is used in the proximity screening of the cathode is difficult and requires additional measures to compensate the residual solenoid field (e.g. bucking coil). Using pulsed solution, the residual magnetic field is well screened by anode and anode support plate.
Confine physical space. To match the electron beam envelope to the first RF accelerating cavity with minimum beam emittance degradation a strong, short as possible, focusing element is
required. The pulsed solution makes possible to have high energy density focusing solenoid in the limited space. The designed eddy current solenoid requires80 mm machine length and volume of 6.3104m3. For comparison a DC solenoid with similar peak magnetic field requires220 mm machine length and volume of 1.5102m3.
Power dissipation. Designed eddy current solenoid dissipates 260 W at maximum magnet current and the total power dissipa- tion including the pulser is 1.4 kW. It is possible to include additional energy recovery system to ‘‘recycle’’ inductively stored energy and to reduce further over all power consumption. For comparison above mentioned DC solution dissipates 3.5 kW and energy recovery is not possible.
No need for mechanical adjustments and correctors. Above described eddy current scheme is capable of suppressing the unwanted transversal magnetic field components and delivers focusing field well aligned with the mechanical axis of the focusing cylinder. This makes alignment of the excitation coil non-critical. If the focusing cylinder is well aligned with the beam axis there is no need for additional mechanical alignment or correction coils. This reduces the mechanical vibration effects and complexity of the machine.
9. Electron beam measurements
For typical operation, amplitude value of the excitation current of 1150 A and a delay time of 8
m
s are used; so there is a large operating reserve. The solenoid field with this condition is 125 mT, requiring a calculated value of cylinder eddy current of 2.5 kA. The delay time and excitation current can be increased together to give the same value of solenoid field at the time of passage of the electron bunch.Unwanted dipole steering was measured as a function of the delay time from excitation current turn-off until electron beam passage. The procedure was the following: a round image of the beam was formed on a Yttrium Aluminum Garnet (YAG) screen 1.18 m downstream from the pulsed solenoid. For given delay times the image diameter was kept constant by adjusting the magnet excitation current. The centroids of these images were measured, including additional steerer offsets needed to keep the image on the YAG screen.
Fig. 9.Long term driftdIexof excitation current maximum value. Sampling rate 2.5 Hz, moving average of 500 samples.
Fig. 10.Electron beam centroid position for different time delay intervals between excitation current turn-off and beam passage for constant focusing field.
Typical results are shown onFig. 10. The expected behavior is that the unwanted transverse field decays more rapidly than the main field.
Taking the standard operating delay setting (8
m
s) and excita- tion current 1.15 kA (125 mT maximum focusing field on axis, field integral on axis 3.16 mT m) the beam deflection is2.5 mm in theX-direction over a distance of 1.18 m, giving 2.1 mrad. For beam energy of 300 kV, this gives a dipole field integral of 4.3m
T m. Using this value, the transverse (dipole) field integral is 1.4 ppt of the main focusing field integral. For the longest delay intervals the transverse field integral approaches 500 ppm of the focusing one.Using the same data, the time constant of the focusing cylinder was found to be 10.470.1
m
s.10. Conclusion
A novel scheme for compact pulsed in-vacuum solenoid is presented where the focusing magnetic field is solely generated by eddy currents. The focusing solenoid is 23.5 mm long with a beam clear aperture of 10 mm. The complete machine length used is 80 mm. It can deliver well aligned solenoid field above 300 mT.
The design does not require mechanical alignment adjustments. Its capability to suppress transverse magnetic field components was studied using physical model measurements and numerical simula- tions. Amplitude jitter and long term stability of the built solenoid satisfy the current machine requirements. Head–tail effects on electron bunches are found to be negligible. Using electron beam measurements it was confirmed that the unwanted dipole field reduces with increase in the delay between excitation turn-off and electron beam passage time.
Pulsed operation scheme makes field screening easy and ensures high energy density of the focusing element. Due to these
features it opens new possibilities for compact focusing solenoids design for single bunch electron guns and linear machines.
Acknowledgments
The authors would like to thank sincerely Walter Pfister and construction office of PSI for their dedication and support for building the pulsed solenoid.
We are very grateful, as well, for the simulation data provided by Frank Weiand and CST Low Frequency Applications Group, which made possible a direct comparison between two different 3D electromagnetic solvers’ results.
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