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**Optimisation of Slow Extraction for SIS-18 and SIS-100**

M. Kirk Synchrotrons Group, GSI Spill intensity 78Kr MeV/u 12C MeV/u Available at

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**Overview Principles of resonant extraction Extraction schemes SIS-18**

Spill-ripple feedback Spill intensity control Spill measurement and analysis Hardt condition SIS-100 “Not so Hardt” condition Power converter ripple (main quadrupoles) RF Knock-Out specification Conclusion & Outlook

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**Resonance Theory – Sextupole Perturbation**

B-field of a sextupole Equation of motion # over circumference: „Tune“ Change variables …

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**Resonance Theory – Sextupole Perturbation**

…to normalized coordinates (u, p) as function of s = point of interest Close to just one resonance (n)

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**Resonance Theory – Sextupole Perturbation**

Change variables (u,p) (r,) to find unstable fixed points (A,B,C) = Separatrix eventually obtaining at the unstable fixed points A,B,C Which yield the conditions on r and …

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**Resonance Theory – Sextupole Perturbation**

… Area of separatrix „Third order/integer“ resonance Normalised sextupole strength Spiral step along the extraction arm > effective septum width!

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**Extraction Methods (M. Pullia) GSI GSI Move machine tune**

Dashed line GSI GSI (Q‘=0) Move machine tune towards resonance. RF acceleration, Longitudinal noise, Betatron core. Transverse RF excitation.

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**RF Knock-Out Extraction**

Transverse Schottky Spectrum PAM spectrum Power density Pick-Up BW (m=0, USB) KO Exc. … ~5 MHz ~300MHz Qf*f0 Qf*f0 (m+1/3)f0 Frequency mf0

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**RF Knock-Out Extraction**

BPSK (GSI) X X‘ Dual FM (HIMAC) Intensity Separate Function not shown.

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**Block Functions of the SIS-18 RF Knock-Out**

P. Moritz, GSI bel.gsi.de/mk/fg/ko_extr.pdf

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Theory Time variation in tune of a bunched beam subject to ripple from the power supplies to the quadrupoles where, Therefore area of separatrix will also oscillate: Thus, to minimize sensitivity to ripple in the quadrupoles, extract with as high S as possible without distortion to the separatrix.

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**Effect of tune ripple on separatrix**

Beam before powering resonance (b) First Extraction Septum Edge Septum change due to tune ripple N Unstable resonant particle at Nth turn (b) (a) 1 4 7 10 …Spill intensity is modulated.

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**Ripple Injection Active ripple excitation (Moritz 2003)**

…spill ripple reduced. Analyzer + generator replaced with feedback amplifier… 300 Hz Traces offset. F/B on Extraction delay determined. Sets limit for spill intensity control. F/B off

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**Spill Analysis DAQ Systems at GSI**

ABLASS / ABLAX TRigger LOgic Pulse Counting NIM modules (discriminator: analogdigital pulse) 4 x 32-bit Multi-Scalers (time slice: bin size) Multi purpose VME module (event decoder) Particles counted: primary beam or secondaries Detectors: Numerous types Detectors at: SIS, HEBT, CAVES Spill intensity versus time Countrate histogram Pulse Counting Detector: Scintillator Pile-up ns CFDFirmware (counting etc.) Particles counted: products Detectors at: LAND, FRS ~ particles per Prim. (FRS) Time interval (pulse-pulse) hist. ABLASS/X Detectors Plastic Scintillator Pulse (ELR) ~20 ns Pulse Counting 1 Pulse per Prim. Mean 106 Prim./s Bin size min. 10 s Ionisation Chamber Pulse (Gas-ions) ~10 s Current-to-Frequency fmax=1 MHz Pulse per Prim. depend on beam Mean Prim./s Bin size >10 s Secondary e- Monitor Pulse (sec. e-) < 10 ns Current-to-Frequency depend on beam Mean >108 Prim./s Bin size >> 10 s

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**Spill detection (P. Forck)**

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SIS-100 Synchrotron Doublet lattice 6 super periods RF-KO

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**Hardt Condition 3 separatrices each with a different momentum**

(Á. Saá-Hernández) Dispersion zero for illustration. Hardt condition.

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**Several Sextupoles Virtual Sextupole**

Driving term (Guignard 1978): Normalised strength: Betatron phase: 1st Extr. Sept. Virtual Sextupole

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**Chromaticity Correction**

in SIS-18: N = # 1C-Sextupoles = # 3C-Sextupoles Adjusted chromaticity (sextupoles on): Natural chromaticity (sextupoles off):

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**SIS-100 Extraction - Powering Scheme**

Lattice version: TDR, Dec 2008 ! RF-KO Exciter Chomaticities: (h), (v). Normalised to tune.

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**Momentum Sensitivity of Separatrix**

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**Optimising the RF Knock-Out Bandwidth**

BW SIS-100: 238U28+ B=100Tm

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**SIS-18 Quadrupoles - Power Converters**

12 pulse SCR power converter 0° (-15) 120° 240° R (magnets + cable) (50 Hz in) Active filter (50-70 kHz) L (magnets) 0° (+15) 120° 240°

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**SIS-18 Quadrupoles - Power Converters**

12-pulse SCR supply. Grid 50 Hz, 3-phase. Main component 600 Hz. Smaller 300 Hz also present. -15 120° +15 30° 120° Active filter reduces U/U0 to <2%

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**SIS-18 Power Converter Ripple**

Measurements taken on the flattop of three machine cycles. Circuit Rigidity B [Tm] 6 10 18 In [A] Freq. [Hz] I [mA] S01QS1F 420 300 0.2 700 1270 600 0.7 0.5 S12QS1F 0.1 S01QS2D 400 0.3 665 1203 0.6 S12QS2D 0.4 1 0.8 S01QS3T 81 137 248 S11MU2 1092 2 1820 4 3340 1050 8 900 F-Quadrupoles 2 Series Circuits D-Quadrupoles 2 Series Circuits T-Quadrupoles 1 Series Circuit Dipoles (H. Welker, H. Ramakers, M. Kirk)

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**SIS-18 Power Converter Ripple**

Measurements taken at constant maximum current in the main quadrupoles. Circuit In [A] I at 300 Hz [mA] I at 600 Hz [mA] S01QS1F 1764 0.5 0.8 S12QS1F 1760 0.2 0.4 S01QS2D 1750 S12QS2D S01QS3T[1] S01QS3T[2] 807 820 0.3 [1] Measured in „computer“ mode. [2] Measured by „hand“. (H. Welker, H. Ramakers, M. Kirk)

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**SIS-100 Quadrupoles - Power Converter**

600 Hz also in SIS-100 quadrupole power converters: 12 pulse line commutated converter (SCR.) Switching Mode (SM) structure: Hard switching. Supplies current to the main quadrupoles. All main quadrupoles but 2 are superconducting. Umax = 640 V at 100 Tm U/Umax = 1% Strongest ripple at f = 600 Hz L = 29 mH (series load) R from connecting cable only. Z 2fL I=U/Z = 59 mA Imax = 7.8 kA (100 Tm) I/I = 7.5x10-6 Closed-loop control has N=18-bit ADC for current measurement. 2N-1 levels from zero to Imax (Unipolar current, Bipolar voltage.) Therefore, minimum possible accuracy is 30 mA During flattop: Magnets are not ramped! 300 Hz component: U/Umax = 0.5% would yield same I

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**Main Quadrupoles – Power Converter Ripple**

SIS-100: 100Tm 238U28+ ions Spill Quality Factor (Imax/Imean) 0.26 (B= Tm)

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**Bunched Beam Extraction**

SIS-100: 238U28+ at 100 Tm F and D quadrupoles: I/I=±10-4

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**Spill Quality - Sensitivity to Momentum Spread**

SIS-100: U (A=238, q=28+) at 100Tm DC beam. Spill Quality Factor (Imax/Imean) RMS Extracted Emittance [mm.mrad]

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**SIS-100 RF Knock-Out System Specification**

P. Moritz, “Detailed Specification on the SIS100 RF KO”, EDMS, GSI-B-RF Systems, 31 Jan 2011

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**Beam Intensity Control**

Open-Loop control. SIS U Tm: Spill Currents KO-Amplitude b>0 b=0 (a=0) t4 Heavyside

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**Beam Intensity Control - Spill Feedback**

Simulation Proportional plus Integral (PI) control: SIS-100: U28+ at 100Tm (VP = 0)

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**SIS-18 Synchrotron Doublet lattice Super periodicity 12**

Sextupoles in odd periods ES SX1 = Res. + Hor. Chro. SX2 = Ver. Chro. FQ = Foc. Quad. DQ = Defoc. Quad. QT = Triplet Quad. ES = Electrostatic Extr. Sept. MS1 = First Extr. Mag. Sept. MS2 = Second Extr Mag. Sept. RF-K.O. = RF Knock-Out Exciter SX1,FQ,DQ,SX2,QT FQ,DQ,QT Injection MS1,MS2 RF-K.O. Reinjection

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**Beam Intensity Control – Feedforward**

Measurement Beam: 12C6+ Energy: ~300 MeV/u C. Bert, A. Constantinescu, D. Ondreka, M. Kirk et al.

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**SIS-18 RF Knock-Out Simulation - Hardt Condition**

181Ta61+ at 300 MeV/u (B=7.97 Tm) DC beam: p/p () = 7.7x10-5 RF Knock-Out: Amplitude (peak) = 2 kV Bandwidth = 6.2 mQ (FW) MAX/AVG: ~14 RMS/AVG: ~230% ~1% of ions lost at extr. septum Bin size 10 s Tunes: (h), 3.27(v) Resonance (1C) + Chromaticity Sextupoles (1C): Amplitude K2L=0.1 m-2 Phase = -161 Offset K2L = m-2 Remaining Chrom (3C) Sextupoles: K2L = m-2

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**SIS-18 RF Knock-Out Simulation - Hardt Condition**

Animation: Horizontal beam phase space with first extraction septum edge (left)

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**Conclusion No real success so far in uniting a good:**

Extraction efficiency, Beamsize, Transmission to target, AND microstructure! Macrostructure at least could be a success story, even for SIS-100.

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**Preliminary Outlook Acknowledgements Code benchmarking**

Other dynamical effects Other extraction techniques, e.g. stochastic extraction Acknowledgements P. Spiller, N. Pyka, P. Moritz, U. Scheeler, G. Franchetti, D. Ondreka, P. Forck, T. Hoffmann, H. Reeg, H. Klingbeil, S. Sorge, E. Feldmeier, A. Dolinskii, H. Eickhoff, T. Furukawa (NIRS), H. Ramakers, H. Welker, Á. Saá Hernández, S. Pietri (FRS), C. Bert, A. Constantinescu, HKR operations crew.

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