2001 immw-xii, oct.1-4, · (a) 32 angular positions, 16 time reads per revolution: allows t = 0.64...

IMMW-XII, Oct.1-4, 2001

Animesh Jain, et al., BNL1

Recent Magnetic Measurement Activities at BNL

Animesh Jain(On behalf of the Magnet Test Group)

Superconducting Magnet DivisionBrookhaven National Laboratory

Upton, New York 11973-5000, USA



Introduction

• Magnetic measurement activities at BNL can be generally classified into three classes, based on the type of magnets measured:(a) Superconducting Magnets (RHIC, LHC, DESY)(b) Conventional Magnets (Spallation Neutron Source)(c) Insertion Devices (G. Rakowsky, National

Synchrotron Light Source at BNL)

• This talk will focus primarily on the recent developments carried out in response to special measurement needs in some superconducting magnets.



Recent Measurements at BNL inSuperconducting Magnets

• “Fast” Measurements for Dynamic Effects(500 µs to 2 sec time resolution; Time decay, snapback, eddy current effects.)

• Helical Dipoles for the RHIC Spin Physics Program (Unusual 3-D field throughout.)Another talk at IMMW12.

• Post-RHIC “Routine” measurements(HERA upgrade magnets, LHC twin aperture dipole prototypes.) Not covered in this talk.



“Fast” Measurements: Dynamic Effects• Time decay of allowed harmonics at injection, and

snapback on resuming the ramp, are well known problems in the use of superconducting magnets in accelerators.

• Typical time decay of harmonics is rather slow several minutes after reaching the injection current. However, the initial decay is much faster.

• Snapback occurs very rapidly, typically over a few seconds.

• Rotating coil systems in routine use at BNL for DC measurements have a period of ~3.5 sec. and can take approx. one reading every minute. A better time resolution is clearly needed to study the dynamic effects.



“Fast” Measurements: Hardware Issues• Harmonics are measured during one rotation of the coil. Coil

should spin as fast as possible to minimize “measurement time”.BNL uses voltmeters, with one power line cycle integration for noise rejection. This limits rotational speed.No. of angular points reduced from 128 to 64 (or 32) to gain a factor of 2 (or 4) in speed.

• Dead time between measurements should be eliminated, thus providing a nearly continuous time map of the harmonics.Modify software to keep acquiring data continuously and storing it in the voltmeters, rather than transfering it to the PC.Amount of data limited by 4K memory of timer card, which stores coil speed information. This memory could not be increased.



Coil Rotation Parameters• Two sets of parameters were used:

(A) 32 angular positions, 16 time reads per revolution:Allows T = 0.64 sec. to 1.0 sec.Continuous data acquisition up to 256 revolutions.Found unsatisfactory for higher order terms, but wasOK for dodecapole in a quadrupole.

(B) 64 angular positions, 32 time reads per revolution:Allows T = 1.28 sec. to 2.0 sec.Continuous data acquisition up to 128 revolutions.Satisfactory for harmonics measurements.



Dynamic Measurements: Analysis Issues• Certain measurements, such as eddy current effects under

ramping conditions, are required to be carried out while the current in the magnet is continuously changing.

• The conventional Fourier analysis, which is used for DC measurements, can not be used to calculate harmonics from the measured coil signals.

• In addition to the current, in general, the harmonics are also time dependent (due to time decay, snapback, superconductor magnetization, etc.)

• This makes a general treatment of the analysis quite difficult.



Approximate Analysis of Data• A simplified scheme has been devised to analyze the data

under the assumption that the Normalized harmonics are invariant during a single rotation of the coil. The absolute values of the harmonics (in Tesla, say) are thus pro-portional to the instantaneous current.The assumption is valid for moderate ramp rates and faster coil rotations.

• The scheme has the advantage of processing data on a rotation by rotation basis.

• The scheme uses Fourier analysis with some manipu-lations of the coil signal to account for the change in current during the measurements.



Tangential Coil Signal in a Varying Field• Field Expansion for the radial component:

C(n,t) = Instantaneous amplitudeαn = phase angle, assumed constant over one rotationRref = reference radius chosen for harmonics

• Coil Parameters:Rc = Radius of the coil∆ = Opening angleN = No. of TurnsL = Lengthω = Angular speed

]sin[),(),,(1

1n

n

n refr nn

RrtnCtrB αθθ −

=

−∞

=∑

Rc

∆

θ

ω

X

Y

Br



Tangential Coil Signal in a Varying Field• Flux through a Tangential Coil:

δ = coil angular position at t = 0 and θ = ω t + δ.• Coil Voltage :

FactorGeometric 2

sin2

)sin(),(1)(1

=

∆

=

−+

=Φ ∑∞

=

nRRRLNG

nntntnCGn

t

n

ref

crefn

nnn

αδω

−+

∂∂

+

−+=

Φ= ∑

∞

=

)sin(),(1

)cos(),()(1

n

nn

nntnt

tnCn

nnntntnCGdtdtV

αδωω

αδωω



Tangential Coil Signal in a Varying Field• Define:

• In terms of these quantities:

−+

+

−+

=∑∞

=

)sin()(

)cos()()()(1

navg

nn

avgavgn

nntnnItR

nntnI

tInCGtV

αδωω

αδωω

( ) ttI/ tRInC

I

avgavg

avg

at time Rate Ramp)(

toingcorrespond strength Harmonic)(

coil theof rotation one duringcurrent Average

=∂∂=

=

=



Tangential Coil Signal in a Varying Field

• V(t), in general, is NOT a periodic function of time.• Coefficients of sine and cosine terms are not constants. Thus

the above expansion is NOT a Fourier series.• Goal is to obtain the quantities Cavg(n) and αn from V(t),

assuming that the current and ramp rate profiles, I(t) and R(t), are known.

−+

+

−+

=∑∞

=

)sin()(

)cos()()()(1

navg

nn

avgavgn

nntnnItR

nntnI

tInCGtV

αδωω

αδωω



Manipulating the Coil Signal

• The right hand side represents a Fourier series.• If the coil signal, V(t), is modified as expressed on the left

hand side, a simple Fourier analysis can be used to obtain Cavg(n) and αn.

• Problem is that this manipulation itself requires the knowledge of Cavg(n) and αn. This problem is solved by using an iterative procedure.

)()(

tII

tV avg∑

∞

=

−+

−1

)sin()()(n

navg

avgn nntnnItRnCG αδω

ωω

∑∞

=

−+=1

)cos()(n

navgn nntnnCG αδωω



Iterative Procedure

• Approximate values of Cavg(n) and αn are first obtained by neglecting the second term on the left hand side.

• The approximate Cavg(n) and αn are then used on the left hand side to obtain new values of Cavg(n) and αn.

• The process is continued until a convergence is reached. Typically, three or four iterations are sufficient.

)()(

tII

tV avg∑

∞

=

−+

−1

)sin()()(n

navg

avgn nntnnItRnCG αδω

ωω

∑∞

=

−+=1

)cos()(n

navgn nntnnCG αδωω



Current Ramps

• Must avoid undershoots and overshoots.

• Two types: “Quadratic” and “Exponential”.

• “Quadratic”: Current Vs time has only linear and quadratic segments.

• “Exponential”: Current Vs time has linear, quadratic and exponential segments.

• Down ramps are always “Quadratic”.



Quadratic Current Ramps• Ramp rate varies linearly with time from zero to Rmax in time t1,

stays constant at Rmax for time t, then goes linearly to zero in time t2.• Characterized by Imin , Imax , Rmax , f1 = t1/(t1+t+t2) and f2 =

t2/(t1+t+t2)• Typically, f1 = f2 = 0.05 to 0.1

0

1000

2000

3000

4000

5000

6000

7000

-100 -50 0 50 100 150 200 250 300 350 400Time (s)

Cur

rent

(A)

0

5

10

15

20

25

30

35

Ram

p R

ate

(A/s

)

CurrentRamp Rate R max

t 2

t 1

t



Exponential Current Ramps• Described in LHC Project Report 172, L. Bottura et al.• Ramp rate varies linearly with time, then exponentially, then stays

constant, then reduces linearly to zero.• Characterized by Imin, Imax, ∆Isn-b, Rsn-b, Rmax, Iexp-max and f4.• Parameters need to be chosen carefully to generate meaningful profiles.

0

1000

2000

3000

4000

5000

6000

7000

-50 0 50 100 150 200 250 300 350 400 450 500Time (s)

Cur

rent

(A)

0

5

10

15

20

25

30

35

Ram

p R

ate

(A/s

)

CurrentRamp Rate



RHIC Quadrupole

-13.0-12.5-12.0-11.5-11.0-10.5-10.0

-9.5-9.0-8.5-8.0-7.5-7.0-6.5-6.0-5.5

0 50 100

150

200

250

300

350

400

450

500

550

Arbitrary Time (sec.)

Nor

mal

12-

pole

(uni

ts a

t 25

mm

)

0250500750100012501500175020002250250027503000325035003750

Cur

rent

(A)

12-PoleCurrent

40 A/s

40 A/s

470 A

3500 A

T = 0.66 sec

QR7109



RHIC Quadrupole

-12.0-11.8-11.6-11.4-11.2-11.0-10.8-10.6-10.4-10.2-10.0

-9.8-9.6-9.4-9.2-9.0-8.8-8.6-8.4-8.2-8.0

350

352

354

356

358

360

362

364

366

368

370

372

374

376

378

380


Nor

mal

12-

pole

(uni

ts a

t 25

mm

)

3003504004505005506006507007508008509009501000105011001150120012501300

Cur

rent

(A)

12-PoleCurrent

T = 0.66 sec

QR7109



RHIC Dipole

-12.5

-11.5

-10.5

-9.5

-8.5

-7.5

-6.5

-5.5

-4.5

-3.5

-2.5

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700


Nor

mal

Sex

tupo

le (u

nits

at 2

5 m

m)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Cur

rent

(A)

SextupoleCurrent

D96525

40 A/s

40 A/s

470 A

5100 A

T = 0.66 sec



RHIC Dipole

-10.2-9.8-9.4-9.0-8.6-8.2-7.8-7.4-7.0-6.6-6.2-5.8-5.4

524

526

528

530

532

534

536

538

540

542

544

546

548

550

552


Nor

mal

Sex

tupo

le (u

nits

at 2

5 m

m)

4004505005506006507007508008509009501000

Cur

rent

(A)

SextupoleCurrent

D96525T = 0.66 sec



RHIC DipoleD96525: Time decay at 470A; 3500A cycle

-10.6

-10.4

-10.2

-10.0

-9.8

-9.6

-9.4

-9.2

-9.0

-8.8

-8.6

-8.4

1 10 100 1000Time (sec)

Nor

mal

Sex

tupo

le (u

nits

at 2

5 m

m) Data

Two Exponentials FitLog(t) Fit (t > 10s)

τ = 45 sec and 303 sec



Prototype Twin Aperture Dipole for LHC

-10.0

-9.5

-9.0

-8.5

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

-200 0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

Time since reaching 300A (sec.)

Nor

mal

Sex

tupo

le (u

nits

at 1

7 m

m)

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

Cur

rent

(A)

1 A/s, with prior quench25 A/s, no prior quenchCurrent (1 A/s case)

Time resolution = 2 sec

DMP402



Prototype Twin Aperture Dipole for LHC

-10.8-10.6-10.4-10.2-10.0-9.8-9.6-9.4-9.2-9.0-8.8-8.6-8.4-8.2

280

290

300

310

320

330

340

350

360

370

380

390

400

410

Current (A)

Nor

mal

Sex

tupo

le (u

nits

at 1

7 m

m)

Decay & Snapback (25A-300A at 1 A/s)Decay & Snapback (25A-300A at 25 A/s)Reference Data (Continuous Ramp at 1 A/s)

DMP402



Eddy Current Effects in DMP402

-0.48

-0.46

-0.44

-0.42

-0.40-0.38

-0.36

-0.34

-0.32

-0.30

1100

1150

1200

1250

1300

1350

1400

1450

1500

1550

1600

1650

Current(A)

Skew

Qua

drup

ole

(uni

t)

Up Ramp 1 A/sUp Ramp 10 A/sUp Ramp 25 A/s



Eddy Current Effects in DMP402

-4.0

-3.9

-3.8

-3.7

-3.6-3.5

-3.4

-3.3

-3.2

-3.1

1100

1150

1200

1250

1300

1350

1400

1450

1500

1550

1600

1650

Current(A)

Nor

mal

Sex

tupo

le (

unit)

Up Ramp 1 A/sUp Ramp 10 A/sUp Ramp 25 A/s



Eddy Current Effects atVery High Ramp Rates

• Focus on Transfer Function, rather than harmonics.

• Measured using non-rotating coil.



Eddy Current Effects: γγγγT Quads in RHIC• RHIC has normal quadrupole correctors which are pulsed

from +50A to –50A in approx. 30 ms as the beam crosses the transition energy.

• This amounts to a ramp rate of ~ 3300 A/s.• It is important to know whether the quadrupole field lags

the current due to eddy current effects.• Difficult to measure harmonics with adequate time

resolution using rotating coils.• We have measured the quadrupole field strength using

stationary quadrupole coils with a time resolution of0.5 ms (500 µs).



Gamma-T Jump in CRF132; Run 41; March 28, 2001Gamma-T Jump from –50A to +50A; Other Supplies at 0 A.

-60-50-40-30-20-10

0102030405060

-25

-20

-15

-10 -5 0 5 10 15 20 25 30

Time (ms)

Cur

rent

(A)

-4000400800120016002000240028003200360040004400

Ram

p R

ate

(A/s)

CurrentRamp Rate




-0.16

-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12

0.16

-25

-20

-15

-10 -5 0 5 10 15 20 25 30 35 40

Time (ms)

Coi

l Sig

nal (

V)

Quad-1Quad-2




-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

-30

-25

-20

-15

-10 -5 0 5 10 15 20 25 30

Time (ms)

Nor

mal

Qua

drup

ole

(T a

t 25

mm

)

-58.5

-48.5

-38.5

-28.5

-18.5

-8.5

1.5

11.5

21.5

31.5

41.5

51.5

Cur

rent

(A)

Normal QuadCurrent




y = 1.3614E-03x - 1.5839E-03

-0.07-0.06-0.05-0.04-0.03-0.02-0.010.000.010.020.030.040.050.060.07

-50

-45

-40

-35

-30

-25

-20

-15

-10 -5 0 5 10 15 20 25 30 35 40 45 50

Current (A)

Nor

mal

Qua

drup

ole

(T a

t 25

mm

) Normal QuadLinear Fit



Magnetic Measurements in Helical Dipoles• BNL is producing 48 helical dipoles for Siberian Snakes

and Spin Rotators to be installed in RHIC under a joint BNL-RIKEN spin physics program.

• The dipole field in these magnets rotates by 360 degrees over a length of 2.4 meters, giving a 3-D field throughout.

• A 51 mm long rotating coil was built for these measure-ments and the analysis was modified for the 3-D field.

• A separate talk at this workshop will give more details.Picture of a helical dipole magnet coil



Conventional Magnets for the SNS• Sector dipole magnets for the Spallation Neutron Source are

being assembled at BNL.• Production measurements will be made using a 2.49 m long,

164 mm diameter rotating coil.• A rectangular aperture requires measurements to be made at

several horizontal positions of the coil.• A built-in horizontal gradient in the integral field implies that

the coil position in the magnet be accurately determined.• The magnet and the rotating coil have survey targets to

determine the coil position with respect to the magnet.• In addition to the dipoles, other magnet types (quadrupoles

and correctors) of various apertures will also be measured for the SNS. (~ 150 magnets total).



Dipole Magnet for the SNS

Survey Survey TargetTarget



Magnetic Measurement Facilities at the National Synchrotron Light Source

• 2.5 m Hall Probe Bench

• Moving-Wire Integrated Multipole Bench

• 2 m Pulsed-Wire Bench

Dedicated to measurement of Insertion Devices and (warm) beam transport and special-purpose magnets

(More information in a talk by G. Rakowsky )



Summary• After the completion of RHIC, recent activities at BNL

have primarily focussed on the study of dynamic effects and on production measurements of helical magnets.

• New hardware and analysis techniques were developed to carry out these measurements.

• Standard measurements were carried out on magnets built at BNL for the HERA luminosity upgrade project.

• Production measurements on conventional magnets for the SNS and superconducting magnets for the LHC have just begun.

2001 immw-xii, oct.1-4, · (a) 32 angular positions, 16 time reads per revolution: allows t = 0.64...

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