Eddy Current Septum Magnet Optimization Powering Options of SMH42 and the Influence of the Septum Thickness on the Fringe Field Zsolt SZOKE (TE/ABT/SE)
Outline • Eddy Current Septa Magnets • Our Goal • Baseline Design Performance • Analysis in Time Domain • Comparing Full Sine and Half Sine Excitation • Comparing 5mm and 3mm Septum Blades • Comparing 2ms and 7ms Wavelength 19/08/2014 LIU-PS Meeting 2
Eddy Current Septa Magnets • Different types of septa: – direct drive (DC, pulsed) – eddy current (only pulsed) • Eddy current type - advantages: – coil dimensions are not critical – the pulsed coil has such a magnetic field which induces eddy currents in the septum counteracting the fringe field – septum can be very thin 19/08/2014 LIU-PS Meeting 3
Our Goal • Optimize different eddy current septum magnet parameters. • 3 comparisons made with the baseline design. • Baseline: 2ms, full sine, 5mm septum. 3mm septum 7ms half sine • Examination of the fringe field: B y and ∫B y dl. 19/08/2014 LIU-PS Meeting 4
Baseline Design Performance • ʃ B y,gap dl max = 502.67Tmm • B y,gap,max = 542mT • ʃ B y,fringe dl max = -1.37Tmm (after the current pulse) • B y,fringe,max = -1.4mT (after the current pulse) • I driving,max = 30251A • Gap fringe field shape: 19/08/2014 LIU-PS Meeting 5
Analysis in Time Domain (1/2) • Opera finite element simulation, spanning 3× the excitation time • Discrete moments interpolation in MATLAB • 2 types of interpolation: – PCHIP: for plotting – SPLINE: for peak determination 19/08/2014 LIU-PS Meeting 6
Analysis in Time Domain (2/2) • 6 values for each simulated moment: – t [ms] – I [kA] “gap”: the middle of the aperture – B y (gap) – ∫B y dl (gap) – B y (fringe) – ∫B y dl (fringe) “fringe”: 5mm from the septum 19/08/2014 LIU-PS Meeting 7
Comparing B y of Full Sine and Half Sine -3 x 10 40 14 • Fringe field extents 30 12 20 10 Magnetic flux density [T] after excitation. 10 8 Current [kA] 0 6 -10 4 -20 2 • Full sine: -30 0 -40 -2 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] B y = -1.4mT 40 0.02 Magnetic flux density [T] • Half sine: Current [kA] 20 0.01 B y = 15mT 0 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] 19/08/2014 LIU-PS Meeting 8
Comparing ʃ B y dl of Full Sine and Half Sine 50 20 • Integrated fringe Field integral [Tmm] field extents after Current [kA] 0 0 excitation. -50 -20 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] • Full sine: 40 20 ∫B y dl = -1.37Tmm Field integral [Tmm] Current [kA] 20 10 • Half sine: ∫B y dl = 14.28Tmm 0 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] 19/08/2014 LIU-PS Meeting 9
Comparing Full Sine and Half Sine • Huge time constants in both cases: – 1 or 2ms excitation time (half or full sine) – time constant: >4ms • Fringe field peak values are 10.4-10.7 times lower using full sine wave instead of half sine. • Using ‘direct damping’ of the fringe field (full sine excitation) proves to be very effective. 19/08/2014 LIU-PS Meeting 10
Comparing B y of 5mm and 3mm Septa -3 x 10 40 14 • Fringe field extents 30 12 20 10 Magnetic flux density [T] 10 8 after excitation. Current [kA] 0 6 -10 4 -20 2 • 5mm septum blade: -30 0 -40 -2 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] B y = -1.4mT 40 0.03 20 0.02 Magnetic flux density [T] • 3mm septum blade: Current [kA] 0 0.01 B y = -3.6mT -20 0 -40 -0.01 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] 19/08/2014 LIU-PS Meeting 11
Comparing ʃ B y dl of 5mm and 3mm Septa 50 20 • Integrated fringe Field integral [Tmm] field extents after Current [kA] 0 0 excitation. -50 -20 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] • 5mm septum blade : 40 30 ∫B y dl = -1.37Tmm 20 20 Field integral [Tmm] Current [kA] 0 10 • 3mm septum blade : -20 0 ∫B y dl = -3.51Tmm -40 -10 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] 19/08/2014 LIU-PS Meeting 12
Comparing 5mm and 3mm Septa • A thinner septum blade is advantageous for the beam: lower continuous losses. • 3 mm septum blade has higher current density. • Fringe field peak values are 1.7-2.6 times lower using 5mm septum instead of 3mm. 19/08/2014 LIU-PS Meeting 13
Comparing B y of 2ms and 7ms Wavelength -3 x 10 40 14 30 12 • Fringe field extents 20 10 Magnetic flux density [T] 10 8 after excitation. Current [kA] 0 6 -10 4 -20 2 -30 0 • 2ms wavelength: -40 -2 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] B y = -1.4mT 40 0.06 20 0.04 Magnetic flux density [T] • 7ms wavelength: Current [kA] 0 0.02 B y = -15.6mT -20 0 -40 -0.02 0 0 5 5 10 10 15 15 20 20 25 25 Time [ms] 19/08/2014 LIU-PS Meeting 14
Comparing ʃ B y dl of 2ms and 7ms Wavelength 50 20 • Integrated fringe Field integral [Tmm] field extents after Current [kA] 0 0 excitation. -50 -20 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Time [ms] • 2ms wavelength : 40 60 ∫B y dl = -1.37Tmm 20 40 Field integral [Tmm] Current [kA] 0 20 • 7ms wavelength : -20 0 ∫B y dl = -15.14Tmm -40 -20 0 0 5 5 10 10 15 15 20 20 25 25 Time [ms] 19/08/2014 LIU-PS Meeting 15
Comparing 2ms Wavelength and 7ms • 3.5 ms pulse half sine shape would be a pulse length similar to present SMH42. • Shorter pulse length (w.r.t. baseline design) wasn’t investigated, since it will be very difficult to build a compatible magnet. • Fringe field peak values are 3.2-11.1 times lower using 2ms full sine wave instead of 7ms. 19/08/2014 LIU-PS Meeting 16
Final Conclusion Full sine vs. Half sine Direct fringe field cancellation very effective 5mm septum vs. 3mm septum The thicker the septum, the lower the fringe field 2ms wavelength vs. 7ms wavelength The shorter the pulse, the lower the fringe field The base line design appears a good compromise. Next: the BMP42 septum bumper analysis. 19/08/2014 LIU-PS Meeting 17
References • Full documentation: Z. Szoke: Eddy Current Septa Magnet Optimization • M. J. Barnes, J. Borburgh, B. Goddard, M. Hourican, in Proceedings of the CAS-CERN Accelerator School: Magnets , Bruges, Belgium, 16- 25 June 2009, edited by D. Brandt, CERN-2010-004, pp. 167-184 • Finite element simulations: Cobham Opera 16 • Data processing: MATLAB R2013b 19/08/2014 LIU-PS Meeting 18
Thank You for Your Attention! Q&A 19/08/2014 LIU-PS Meeting 19
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