1. The AC Dipole system for LHC Technology and operational parameters Javier Serrano AB-CO-HT LHCCWG 10 April 2007

2. 10 April 2007LHCCWG meeting2 of 22 Outline Introduction. Key stakeholders. Technical specifications. Proposed solution. Center frequency choices. Ongoing developments. Outstanding issues. Planning for the rest of 2007.

3. 10 April 2007LHCCWG meeting3 of 22 Introduction AC dipole: a dipole magnet excited with an oscillating current. If the excitation frequency is close to the tune, a driven coherent oscillation of the beam results. If the excitation amplitude is ramped up/down adiabatically, beam emittance is preserved. In 2006 AB-BT agreed to let AB-CO use the MKQA magnets as AC Dipoles. A set of relays selects among three generators (Aperture, Q, AC Dipole) to drive one magnet. The LHC AC Dipole project was endorsed by the LTC on 13/09/2006 with the goal of having a system ready for LHC commissioning. (http://ab-div.web.cern.ch/ab-div/Meetings/ltc/ltc_2006-11.html)http://ab-div.web.cern.ch/ab-div/Meetings/ltc/ltc_2006-11.html

4. 10 April 2007LHCCWG meeting4 of 22 Key stakeholders AB-ABP: will we have enough power in the AC Dipole to perform all the measurements we want? Contacts: Rogelio Tomás, Stéphane Fartoukh. Machine protection: will the AC Dipole be properly designed so as to minimize the risks of machine damage? Contacts: Rüdiger Schmidt, Jörg Wenninger, Jan Uythoven. AB-BT: will the Q and aperture generators be affected by the installation of the new AC Dipole generator in the same rack? Contacts: Gene Vossenberg, Etienne Carlier. AB-OP: how will the AC Dipole system be operated? Contact: Jörg Wenninger. US-LARP: can these developments benefit the existing AC Dipoles in FNAL and BNL? Contacts: Andreas Jansson, Ryoichi Miyamoto, Sacha Kopp, Mike Syphers (FNAL), Mei Bai, Rama Calaga, Peter Oddo (BNL).

5. 10 April 2007LHCCWG meeting5 of 22 Technical Specifications (1/2) Integrated field strength necessary to generate a transverse displacement Δ z using an AC-Dipole Where: Bρ is the magnetic rigidity: 1501 Tm for LHC at 450 GeV. δ is a relative measure of the distance in frequency between the B field and the tune: spec says 0.025. β z is the value of the betatron function at the location of the AC-Dipole. In our case, of the four magnets the worst (lowest) case is 258.4 m. Δz is specified as 7σ in the AC Dipole location at 450 GeV, i.e. 9.87 mm. Bl(max) = 18.01 mT·mI(max) = 1733 A I(rms) = 1225 A NB1: in order to generate a displacement of 4 sigma at 7 TeV with δ=0.01 (previous spec) a Bl of 16.35 mT·m is enough. NB2: The specified Bl at injection corresponds to a “kick per turn” of 12 μ rad.

6. 10 April 2007LHCCWG meeting6 of 22 Technical specifications (2/2) H tune foreseen between 0.28 (450 GeV) and 0.31 (7 TeV). V tune foreseen between 0.31 (450 GeV) and 0.32 (7 TeV). Total tunable range, including going to δ=0.025 on either side: 0.08 tune units, i.e. 11245 * 0.08 = 900 Hz. We propose an RCL resonator (see next slides) with C chosen to set the center frequency at 0.295 for the horizontal systems and at 0.315 for the vertical ones. Current at peak should be enough to guarantee 1225 A rms at ±450 Hz frequency offset. If OP decides to work on other tunes, we have to go and change some caps. Special attention given to tune range 0.2-0.4. Ongoing work at BNL to study variable capacitors and inductors (more on this later). The specified excitation takes the shape of a sine wave with a trapezoidal envelope. To maintain adiabaticity, rise and fall times of 200 ms or longer are acceptable.

7. 10 April 2007LHCCWG meeting7 of 22 Proposed solution (1/4): parallel RCL circuit Rs jXs RpjXp This......is the same as this

8. 10 April 2007LHCCWG meeting8 of 22 Proposed solution (2/4): quality factor definitions ω ωrωr Z BW or The current in L P is Q times the current in R P, i.e. this circuit works like a current amplifier. Note that Q is unchanged under series to parallel transformation, as long as it’s defined as ω r L S /R S for the series configuration.

9. 10 April 2007LHCCWG meeting9 of 22 Proposed solution (3/4): audio amplifiers and transformers Switching (class D) audio amplifiers are available with several kW of power:  I-T8000 from Crown: 8kW amplifier used at FNAL and CERN. http://www.crownaudio.com/amp_htm/itech.htm http://www.crownaudio.com/amp_htm/itech.htm  FP 13000 from Lab.Gruppen: 13 kW, being tested at CERN. http://www.labgruppen.com/Default.asp?Id=9024 http://www.labgruppen.com/Default.asp?Id=9024  DIGAM K18 from Powersoft, upcoming, not yet in their website: 18 kW. http://pro-audio.powersoft.it/an_series_list.php?use_in=53&id_menu=271&obj=12 http://pro-audio.powersoft.it/an_series_list.php?use_in=53&id_menu=271&obj=12 These amplifiers are current-limited for low R p and voltage limited for high R p, i.e. they have a “preferred” R p to deliver maximum power. Transformers are needed to:  Transform our initial R p into the one the amplifier likes.  Use the amplifiers in mono bridge mode (our magnet is returned to ground).  Couple the power of more than one amplifier into the load (more on this later). A transformer does not change the Q of the circuit. It just trades current for voltage, maintaining constant power (for a perfect transformer, that is).

10. 10 April 2007LHCCWG meeting10 of 22 Proposed solution (4/4): design procedure Assume you can match the load to the generators, so worry only about power needs and power ratings. Measure R P and Q for the magnet at the desired frequency. If I magnet is the specified rms current for the magnet, the needed power is P=(I magnet /Q) 2 · R P This is only a first estimate, because the resulting circuit will deliver I magnet only at the frequency of the peak. We want I magnet at ±450 Hz from the peak. Choose the appropriate C p to make the circuit resonate with L p at the chosen frequency, and simulate. Read the I magnet current at ±450 Hz from the peak and scale the power requirement accordingly. Choose amplifier(s) and transformer(s) to deliver enough power to the matched load.

11. 10 April 2007LHCCWG meeting11 of 22 Center frequency choices According to AC Dipole theory, and assuming a tune of 0.3 in the LHC, the AC Dipole generator can work at 4 different frequencies in the audio (0- 20kHz) range:  f1 = 11245 * (0 + 0.3) = 3.37 kHz  f2 = 11245 * (1 – 0.3) = 7.87 kHz  f3 = 11245 * (1 + 0.3) = 14.62 kHz  f4 = 11245 * (2 – 0.3) = 19.12 kHz Q usually grows with frequency, although slower than ω due to skin effect. BW = (f R /Q) also grows, although again slower than ω. However, the rise of R s -R DC with sqrt(ω) (skin effect) means more losses at high frequencies. The best thing is to test and simulate using test results. Tests are easier if we get higher currents by inserting a C in parallel to the circuit under test, but our current choice for C values is limited...

12. 10 April 2007LHCCWG meeting12 of 22 Test at f=2.9 kHz (close to f1) C = 760μF (3*120μF + 4*100μF) Q(measured)=6.35 Rp(measured)=0.462 Ohm Courtesy of Matthieu Cattin

13. 10 April 2007LHCCWG meeting13 of 22 Test at f=8.2 kHz (close to f2) C = 120μF (1*120μF) Q(measured)=10.2 Rp(measured)=1.677 Ohm Courtesy of Matthieu Cattin

14. 10 April 2007LHCCWG meeting14 of 22 AC Dipole Test Stand in building 867

15. 10 April 2007LHCCWG meeting15 of 22 Coupling many amplifiers This is the way they couple amplifiers in BNL, except they couple 24 250W amplifiers for a total power of 6kW. FNAL is also working on this for their AC Dipole.

16. 10 April 2007LHCCWG meeting16 of 22 Back to our measurements f (kHz)2.98.2 C (uF) (notice slight cheating to fit rest of data)754.3169791118.052011 Q6.3510.2 Rp (mOhm)4621677 Magnet current needed (A rms)1225 Power needed (kW)17.1935953924.1882749 Xp (mOhm)72.75590551164.411765 Lp (uH)3.9929179313.19109086 Rs (mOhm)11.1803496915.9653465 Xs (mOhm)70.99522052162.846535 Ls (uH)3.8962897523.16071109 Preferred load for the amp (Ohm)44 Optimal N1/N2 for 2 transformer arrangement with secondaries in series4.1612518932.18412989 Impedance transformation ratio17.316017324.77042338 Let’s take these numbers and simulate what two FP 13000 amplifiers can deliver to the magnet under these conditions.

17. 10 April 2007LHCCWG meeting17 of 22 Simulation for f = 2.9 kHz case NB: only 0.05 tune units shown

18. 10 April 2007LHCCWG meeting18 of 22 Simulation for f = 8.2 kHz case

19. 10 April 2007LHCCWG meeting19 of 22 Comparison Near delta=0, lower losses favor f=2.9 kHz. Far away, the higher BW at f=8.2 kHz takes over. Tough choice!

20. 10 April 2007LHCCWG meeting20 of 22 Ongoing developments Coupling two amplifiers together and checking reality vs. simulations. Transformers should arrive at CERN anytime now. FNAL is also studying this. Variable capacitors and inductors. Contact: Peter Oddo (BNL):  Variable capacitors: C in series with switch. Effective C depends on switch’s duty cycle.  Variable inductors (1): make a core saturate, therefore losing its inductance, a certain percentage of time, with the help of an auxiliary DC winding. This is ON/OFF control as with the capacitor.  Variable inductors (2): with an auxiliary winding carrying a DC current, go to a certain point in the core’s B-H curve. Incremental inductance can be controlled in this way.

21. 10 April 2007LHCCWG meeting21 of 22 Outstanding issues Test relay to verify it does not heat up too much (Ross model EA12-NO-20- 2C-78A-BU). Have software avoid too frequent excitations if need be. Measure magnetic field in the magnet to make sure our amps to T*m conversion factor is correct. β-beating at injection can be ±15%. Adjust specs accordingly to meet 7σ spec for worst-case β at injection? Organize cabling of AC Mains in UA43 (cable from AB-BT’s racks). Work on strategies to follow tune during LHC startup. Try to get hold of the new 18 kW amplifiers for test. Work with machine protection. Items for discussion include:  Constrain possible values of excitation by reading current Energy & Intensity in the front end.  Decide on final strategy for AC Dipole/Aperture/Q measurement selection button location(s).  Avoid collision with other interlocks (e.g. dump channel BPMs fire at Δz=3mm with unsafe beam).  Software could enforce a Q measurement before use.

22. 10 April 2007LHCCWG meeting22 of 22 Planning: tentative dates End of the year (2007) → have it ready, which means:  SW specs with OP, then find someone to develop, hopefully before beginning of Summer.  start working with MPWG right away.  Working prototype, with acceptable power, at the end of the Summer.  Installation in the four AB-BT generator racks in November.  HW/SW commissioning in December.

23. 10 April 2007LHCCWG meeting23 of 22 Reserve slides MKQA magnet parameters (courtesy of Gene Vossenberg). FNAL system (courtesy of Andreas Jansson and Ryoichi Miyamoto). BNL system (courtesy of Mei Bai). UA43 rack layout (courtesy of Etienne Carlier). MKQA misc info, courtesy of Gene Vossenberg.

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28. 10 April 2007LHCCWG meeting28 FNAL AC Dipole Generator 2.5μH6μF6μF65mΩ8.3μH 8.2μF Power SupplyMagnet + Cables 20kHz CT Schematic Diagram and Picture of the Circuit Z tot ≈ 10 Ω R+X L = 1 Ω I magnet = V amp / (R+X L ) ≈ 100 A Courtesy of A. Jansson and R. Miyamoto

29. 10 April 2007LHCCWG meeting29 RHIC AC Dipole system Courtesy of M. Bai

30. 10 April 2007LHCCWG meeting30 UA43 rack layout

31. 10 April 2007LHCCWG meeting31 Misc info on MKQA Maximum flux in the steel tape cores of MKQA is 1100mT. Stacking factor is 0.88 and due to gap geometry 4% is lost. This means max. flux in gap is 930mT. With corresponding magnetic length of 0.614m, the max. kick is 571mT m.