Beam Current Monitors

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1 Beam Current Monitors Accelerator Beam Diagnos4cs W. Blokland (ORNL) USPAS and University of New Mexico Albuquerque NM, June 23 26, 2009 USPAS09 at UNM Accelerator and Beam Diagnos4cs 1

2 Beam Current Monitors Why use Beam Current Monitors? How to couple to the beam Transformer Resis4ve Wall Current monitor Faraday Cups Limita4ons: Noise, bandwidth Lab USPAS09 at UNM Accelerator and Beam Diagnos4cs 2

3 Par4cle Accelerators One measure of performance: Power The amount of particles delivered at a certain energy. SNS Power on target SNS Energy delivered to target USPAS09 at UNM Accelerator and Beam Diagnos4cs 3

4 Par4cle Accelerators How well do you accelerate beam? What percent of the particles make it to the end Effectiveness of acceleration process. E.g. stripping losses 3-5% of beam What percent of time are you operational? Damage to accelerator What is the quality of your beam? Emittance (collider) Density profile (target) Position stability Radio-activation USPAS09 at UNM Accelerator and Beam Diagnos4cs 4

5 Charged Beam What is the beam current? I beam = qen t = qen l βc In an accelerator the current is formed by N par4cles of charge state q per unit of 4me t or unit of length l and velocity β = v/c. The beam is nearly an ideal current source with a very high source impedance We can measure the beam through the electric and magnetic fields created by the beam. USPAS09 at UNM Accelerator and Beam Diagnos4cs 5

6 Beam Current Structure SNS Beam Structure USPAS09 at UNM Accelerator and Beam Diagnos4cs 6

7 Beam Image currents [5] [5] Moving charge Fast moving charge Fast moving par4cles (moving E field) create an H field. The H field moves the E field induced image charges. At high veloci4es the wall current spectrum is an image (opposite sign) of the beam spectrum: at at a speed of 0.5c, approx RMS length is 90ps or 1.8GHz USPAS09 at UNM Accelerator and Beam Diagnos4cs 7

8 Beam Image currents If the wall current mirrors the beam current then the magne4c field outside the beam pipe is cancelled: Ampere's Law : H dl = I and with I beam = - I image then H dl = I beam + I image = 0 H = 0 Is it completely cancelled? Skin depth: the length in which the fields are reduced by a factor of e ( 8.7 db). At 10Mhz, a typical 0.794mm stainless pipe aeenuates 53dB. δ = π ρ f with ρ the resistivity and f the frequency From [2] Webber. USPAS09 at UNM Accelerator and Beam Diagnos4cs 8

9 Beam Pipe Break No field outside of beam pipe. Either: install detector inside beam pipe or Inside beam pipe means installa4on in vacuum use a ceramic break Ceramic break forces image current to find another path and it will do so! Z gap USPAS09 at UNM Accelerator and Beam Diagnos4cs 9

10 You beeer define your gap impedance. Something will always be present, such as a path to ground and capacitance. Z gap is combina4on of the gap capacitance and all external parallel elements Gap voltage Gap Impedance Courtesy of Jim Crisp & Mike can be generated up to beam voltage Z gap USPAS09 at UNM Accelerator and Beam Diagnos4cs 10

11 Current transformer Measure the beam current through the magne4c field of the beam. Assume the beam is long enough to be regarded as a line current. E.g. SNS Ring: 250 meters for 1usec Line current field : B = µ I beam 2πr a ϕ [1] Β Torus to guide the magnetic field I beam R v out USPAS09 at UNM Accelerator and Beam Diagnos4cs 11

12 V p I p Primary winding N p turns H N turns Current transformer toroid material permeability = µ 0 µ r cross section = A Mean radius = r I s I p R s R s Secondary winding N s turns Integration path dl v s V s Ampere s Law: H dl = N p I p + N s I s = I p + N s I s with N p =1 H = (I p + N s I s ) /2πr (1) Φ = Flux: (thin toroid approxima4on) ds= µha = µa(i p + N s I s ) /2πr with A as area (2) B S Faraday s Law: V s = N s dφ dt = I s R s (3) Combine (2) and (3): I s R s = N s µa 2πr d(i + N I ) p s s dt Differen4al equa4on: di s dt + R s I s = 1 di p L s N s dt Laplace rewrite: I s (iω) I p (iω) = 1 N s iω (iω + R s /L s ) with L s = N 2 sµa 2πr USPAS09 at UNM Accelerator and Beam Diagnos4cs 12 (4)

13 Current transformer Great, we got our transfer function and now we can figure out what the behavior is of our current transformer: I s (iω) I p (iω) = 1 N s iω (iω + R s /L s ) When Power: iω >> R s /L s P s = I 2 s R s = I 2 p N R 2 s s I s = I p N s (transferred from beam) USPAS09 at UNM Accelerator and Beam Diagnos4cs 13

14 Current transformer The inductance plays an important role in the design of transformer. Note that in the calculation for inductance, the geometry of the setup plays and important role as well as the µ and windings. Inductance of a torus with a square cross section: Φ = B ds= S µhds = S µi 2πr ldr = µi 2π lln r out r out with L = NΦ then I L = µn 2 l 2π ln r out and µ = µ 0 µ r r in r in r in µ r can be > ι ds r in µ r r out L s = N s 2 L p USPAS09 at UNM Accelerator and Beam Diagnos4cs 14

15 Current transformer Too bad there is also a capacitance: we get an LCR circuit: [1] 1 Z = 1 R + 1 iωl + iωc iωl Z = 1+ iωl /R (ωl /R) (ωrc) USPAS09 at UNM Accelerator and Beam Diagnos4cs 15

16 LRC Proper4es What are proper4es of an LRC circuit? iωl Z = 1+ iωl /R (ωl /R) (ωrc) For low frequency : ω << R /L Z = iωl For high frequency : ω >>1/RC Z =1/iωC For mid frequency : R /L << ω <<1/RC Z R It s a band pass with a: droop 4me t droop rise 4me t rise log [5] R/L 1/RC ω USPAS09 at UNM Accelerator and Beam Diagnos4cs 16

17 Bandpass effects on pulse shape USPAS09 at UNM Accelerator and Beam Diagnos4cs 17

18 Rise 4me and droop 4me Rise 4me t rise : defined as the 4me it takes the amplitude to go from 10% to 90%. Rise 4me constant τ rise : and τ A (1 e t /τ rise ) rise corresponds to the 4me for an increase by e 1 = 37 %. t rise = ln0.9 ln0.1 ω high = ω high = πf high ω high =1/RC t rise 2RC 1 3 f high or t rise 2τ rise with τ rise = RC Droop 4me t droop = ω low = R /L ln0.9 ln0.1 ω low = ω low = πf low 1 3 f low t low 2L /R or t low 2τ low with τ low = L /R USPAS09 at UNM Accelerator and Beam Diagnos4cs 18

19 Current Transformer Add (long) cable to current transformer: add cable resistance, capacitance and inductance: τ rise = L s C s τ droop = L /(R +R L ) [1] Ac4ve Transformer: use a trans impedance circuit to lower the load impedance. τ droop = L /(R f / A +R L ) = L /R L [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 19

20 Design of Current Transformer How to design a current transformer: High sensi4vity > low number of turns, low N s High droop 4me > high L > high µ, high N s τ droop = L s /R s V s = I s R s = I b N s R s L s = l 2π ln r out 2 µ N s Fast rise 4me > low stray capacitance r in τ rise = L s C s with cable τ rise = RC without cable USPAS09 at UNM Accelerator and Beam Diagnos4cs 20

21 Design of Current Transformer Passive transformer Ac4ve transformer USPAS09 at UNM Accelerator and Beam Diagnos4cs 21

22 DC Current Transformer How to measure the DC current? The current transformer discussed sees only changes in the flux. The DC Current Transformer (DCCT): look at the magne4c satura4on of the torus. Modula4on of the primary windings forces the torus into satura4on twice per cycle. Secondary windings sense modula4on signal and cancel each other. But with the I beam, the satura4on is shiued and I sense is not zero Adjust compensa4on current un4l I sense is zero once again. DC Transformer Opera4on, see [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 22

23 DC Current Transformer Example bandwidth: DC to 20kHz, resolu4on 2µA [1] Modula4on of the primary windings forces the torus into satura4on twice per cycle. Secondary windings sense modula4on signal and cancel each other. But with the I beam, the satura4on is shiued and I sense is not zero Adjust compensa4on current un4l I sense is zero once again. USPAS09 at UNM Accelerator and Beam Diagnos4cs 23

24 Current Monitor Limita4ons Limita4on to transformers: The permeability of a core can be saturated: specs of max B field or max current 4me product I*t, Thermal noise: V n 4k b Tf high R -> µa range lower limit Weiss domains lead to Barkhausen noise if termina4ng with high impedance (limit for DC type) Avoid external magne4c fields Torus material has dependency of µ r on temperature or on mechanical stress (micro phonic pickup) Avoid secondary electrons from being measured USPAS09 at UNM Accelerator and Beam Diagnos4cs 24

25 BCM Tes4ng Fixture Image by M. Kesselman USPAS09 at UNM Accelerator and Beam Diagnos4cs 25

26 SNS Current Transformer Image by M. Kesselman. USPAS09 at UNM Accelerator and Beam Diagnos4cs 26

27 LHC Fast Current Transformer U. Raich CAS Frasca Beam Diagnos4cs USPAS09 at UNM Accelerator and Beam Diagnos4cs 27

28 COMPONENTS INSIDE HEBT BCM ASSEMBLY Design by BNL for SNS USPAS09 at UNM Accelerator and Beam Diagnos4cs 28

29 Wall Current Monitor Put a resistor over the gap and measure its voltage. V gap = R gap I beam V out R No DC in image current USPAS09 at UNM Accelerator and Beam Diagnos4cs 29

30 Wall Current Monitor U. Raich USPAS09 at UNM Accelerator and Beam Diagnos4cs 30

31 Wall Current Monitor Now for the details: Ceramic gap to avoid working in vacuum Distributed resistors (30 to 100) for beam posi4on independency Ferrite rings for low frequency response Shield for ground currents and noise protec4on Schema4cs of a wall current monitor and its equivalent circuit [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 31

32 Wait, there is more I in /n Broadband Model [4] 2ζ= (R L / R L + R s )((R s C/L e + (1/ R L ) L e /C) ω o = 1/(R L / R L + R s ) L e C I in /n Even a resistor is not a resistor: Low to Midband Model [4] USPAS09 at UNM Accelerator and Beam Diagnos4cs 32

33 Faraday Cups The Faraday Cup destruc4vely intercepts the beam DC coupled! (With just a resistor the signal is V out = I beam *R) Low current measurements possible e.g., 10pA Problem with secondary electrons: - Use long cup or voltage suppression or magne4c field If not properly terminated > very high voltage (beam poten4al) Must process beam power (SNS full power 1.4MW) [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 33

34 Faraday Cups Low power Faraday Cup [1] High power (1MW) Faraday Cup [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 34

35 Noise Issues Noise can be a problem! There are many powerful noise sources in Accelerators: - Switching power supplies - Accelera4ng RF - Source RF Case in point: - SNS DTL BCM > single ended and inside a cavity (due to space limita4ons) USPAS09 at UNM Accelerator and Beam Diagnos4cs 35

36 Noise Issues Noise from switching power supplies Grounded [8] USPAS09 at UNM Noise from RF Beam Noise of DTL current transformer (inside cavity, single ended) Accelerator and Beam Diagnos4cs 36

37 Noise Issues Beam SCL Beam Current Monitor (single ended) USPAS09 at UNM [8] Accelerator and Beam Diagnos4cs 37

38 Noise Issues Beeer: CCL BCM outside of cavity but s4ll single ended. Beam CCL Beam Current Monitor (single ended) USPAS09 at UNM Accelerator and Beam Diagnos4cs 38

39 Noise Issues: Common Mode If noise is coupled into both wires, we can reject it! > common mode noise rejec4on by taking the difference. You will do this as a lab experiment. 20mV 2mV 20mV Differen4al noise on long twinax with far end shield grounded. Leu: top and boeom, noise on either center conductor into 50 ohms (each 20mV/div); center, difference (2mV/div); (most of residual signal due to digital scope subtrac4on). Right: same signals faster 4me scale (each 20mV/div and 1uS/div). From [2] Webber. USPAS09 at UNM Accelerator and Beam Diagnos4cs 39

40 References [1] Forck P., Lecture Notes on Beam Instrumenta4on and Diagnos4cs, Joint University Accelerator School, [2] Webber R.C., Tutorial on Beam Current Monitoring, BIW 2000, pp [3] Webber R.C., Charged Par4cle Beam Current Monitoring Tutorial, BIW1994, pp 3 23 [4] Webber R.C., Longitudinal Emieance: An Introduc4on to the Concept and Survey of Measurement Techniques, Including Design of a Wall Current Monitor BIW 1993 [5] Denard, J.C. CERN Accelerator School on Beam Diagnos4cs, 28 May 6 June 2008, Dourdan. [6] Hammond P., Electromagne4sm for Engineers, Pergamon Press. [7] Waters C., Current Transformers provide accurate, isolated Measurements, Power Conversion& Intelligent Mo4on, Issue December 1986 [8] Plum M., LANL Current Monitor Pickup Final Design Review, March [9] Edminister J., Schaum's Outline of Electromagne4cs BCM Lunch4me Seminar 40

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