TESLA COIL DESIGN FOR ELECTRON GUN APPLICATION Part of Low Emittance electron Gun Project ξ
M. Paraliev , C. Gough, S. Ivkovic Paul Scherrer Institute, Accelerator Division, 5232 Villigen PSI, Switzerland
Abstract
RESONANT AIR-CORE TRANSFORMER (Tesla Coil)
The current project is to build an electron gun for X-ray Free Electron Laser (XFEL) application. The electron gun will utilize field emission and extreme accelerating gradient to achieve very low emittance. However for long-term study of cathode characteristics, a stable pulsed voltage in the megavolt range is needed. The first project phase is to design and test a 500kV pulser using a resonant aircore transformer (Tesla coil). Detailed results of simulations with Microwave Studio® and PSpice® for various coil geometries, tuning and coupling factors are given, and the optimum values for this application are given. In addition, experimental results are given for the most promising geometries.
Tesla Coil:
Differential System:
Critical Case:
Simplified Circuit:
1.2
u1 u2
Normalized Amplitude
0.8 0.4 0 -0.4 -0.8
Solution:
-1.2 0
1
2
3
Cycles
Equivalent Circuit:
.
Tesla’s Patent:
PARAMETRIC STUDY
SIMULATION AND EXPERIMENTAL RESULTS
PSpice® simulation circuit
Microwave Studio® coil model
Coupling comparison
Measurement
0.85
Coupling
Simulation
Multilevel Subgirding Scheme meshing Electromagnetic simulation
Upos
0.9
0.80 0.75 0.70 0.65 0.60 0
4
8
12
16
20
24
Turns
Measurement and simulation based results (with the simulation time).
In order to calculate the coupling a shorting conductor is needed.
1.2
Amplitude (Arbitrary Units)
Typical waveforms of primary (u1) and secondary (u2) voltage Cp = 250%.C K = 0.55
0.90
0.6 0.3 0.0 -0.3 -0.6
u1 u2
Uneg
-0.9 -1.2 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
120.0
Amplitude (Arbitrary Units)
Frequency response of the transformer Cp = 250%.C K = 0.55
Air-core geometry comparison. Helical and spiral (with central and peripheral excitation) autotransformers with one turn primary.
1.871 MHz
100.0
2.055 MHz
0.935 MHz
80.0
Coupling
Time, μs
1.00
Measured Samples.
0.80
Conductors Span is kept 15mm for all coils.
0.60 0.40
Spiral Peripheral
0.20
Helix Spiral Central
60.0
0.00
40.0
0
2
4
6
20.0
8
10
12
14
Turns
Spiral Coil, Copper Round Ø9mm, Dm 380mm
0.0 1.5
2.0
2.5
3.0
Frequency, MHz
Normalized secondary peak voltage amplitude as function of coupling and primary capacitance with 30% loss factor
Negative to positive peak voltage ratio of secondary voltage oscillation as function of coupling and primary capacitance with 30% loss factor
Abs. Ampl. Maximum
Conductor profile comparison. Round vs. strip conductor on conditions that the conductor cross-section perimeter is the same (for spiral and helical geometry).
1.00
Coupling
1.0
Helical Coil, Copper Rund Ø9mm, D 380mm
0.80 0.60
Spiral Round Ø9 Spiral Strip 14x1 Helix Round Ø9 Helix Strip 14x1
0.40 0.20 0.00 0
2
4
6
8
10
12
14
Spiral Coil, Copper Strip 14x1mm Dm 380mm
Turns
Conductor profile comparison. Two different strip widths are compared (for spiral and helical geometry)
Helical Coil, Copper Strip 14x1mm, D 220mm
1.00
Coupling
0.5
0.80 0.60
Spiral Strip 50x1 Spiral Strip 14x1
0.40
Helix Strip 50x1 Helix Strip 14x1
0.20 0.00 0
2
4
Abs. Ampl. Maximum
6
8
10
12
14
Spiral Coil, Copper Strip 50x1mm Dm 380mm
Turns
Coil diameter comparison (for two strip widths.) Scaling of air-core transformers 600 Lp(sh), nH 500
Coupling, x1000
Helical Coil, Copper Strip 50x1mm, D 220mm
1.00
Coupling
0.0
0.80 0.60
Helix Helix Helix Helix
0.40 0.20
Lp, nH
400
D380 Strip 14x1 D220 Strip 14x1 D380 Strip 50x1 D220 Strip 50x1
Helical Coil, Copper Strip 14x1mm, D 380mm
0.00
300
0
200
2
4
6
8
10
12
14
100 0 0
20
40
60
80
100
120
Turns
Coil Perimeter, cm
Output pulse amplitude and shape are sensitive to the coupling and relatively less sensitive to primary capacitance. To obtain large negative to positive peak voltage ratio of the output pulse, the coupling factor should be kept within 0.58 to 0.62. Larger value of primary capacitance, with respect to the tuned value, gives an improvement in amplitude and the change of the shape of the output voltage oscillation could be compensated, to certain extend, by decreasing the coupling.
ξ
email:
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CONCLUSIONS The spiral geometry with peripheral excitation gives the best coupling for given dimensions and conductors span. Wider strips give better coupling. The influence of the conductor cross-section profile on coupling is small on conditions that the conductor cross-section perimeter is the same.
Helical Coil, Copper Strip 50x1mm, D 380mm
With increase of number of turns the coupling decreases. The studied shapes sowed that the increase of number of turns more than 20 is inefficient. Scaling the size of the transformer gives a linear scaling of all self and mutual inductances but doesn’t change the coupling. Difference between calculated coupling factors based on Microwave Studio® simulations (with fixed mesh) and measurements is less than 1%.
PPC 2005
