RFQ Tuning Method last results

CEA Saclay / F. SIMOENS - A. FRANCE - J. GAIFFIERRFQ tuning method 10/02/2003

RFQ Tuning Methodlast results

IPHI-SPL collaboration meeting - CERN 28 & 29 /04/2003

CEA/DSM/DAPNIA/SACM


What do we electromagnetically tune ?

2. Accelerating voltage profile : Vp(z)

|(uQ(z)-Vp(z))/Vp(z)|< 10-2

4. Closest dipole modes frequencies

f +D - fQ = fQ - f -

D

352.21 MHz1. Resonance Frequency fQ :

3. Dipole components presence within the accelerating mode

|uS(z)/uQ(z)|< 10-2 |uT(z)/uQ(z) |< 10-2

80

90

100

110

120

130

0 1 2 3 4 5 6 7 8

V [kV]

z [m]


S = [ -1/2, 0, 1/2, 0]

T = [ 0, -1/2, 0, 1/2] S

0V

0V

Et

Ht

R(Hz)

+

+

-

-

Mode S et T (ST)

distribution S

dipole Modes

Q = [ -1/2, 1/2, -1/2, 1/2]

Mode Q

0V 0V

0V 0V

-

-

+ +

Et

Ht

R(Hz)

Quadripole Mode focalisation Kpq = 352,2 MHz

…


Central region

What do we mechanically tune ?

1. Slug tuners

End regions

2. « dipole » rods

3. Plate thickness


The tuning tools that we have developed

1. Model

What is the

ideal RFQ ?

Diagnosis

Treatment

2. Test bench

e.l.m. parameters

of the real RFQ

3. Spectral analysis Defaults real RFQ / ideal RFQ

e.l.m. parameters mechanical devices

5. Mathematical formalism

4. Cold-model Frequencies

Field distribution

1. Slug tuners

2. Dipole rods

3. End plates

Fast tuning High accuracy


Our model & the associated spectral analysis

Refer to :A. France, F. Simoens, “Theoretical Analysis of a Real-life RFQ Using a 4-Wire Line Model and the Spectral Theory of Differential Operators.”, EPAC2002 Conference (Paris), June 2002

Coupled, inhomogeneous,

4-wire line equivalent circuit

Central region End regionsEnd regions

Eigen functions (orthogonal basis)

= { vQi(z), vSj(z), vTk(z) }

voltage base functions

'2

2' Vc

VM

M = hermetian operator (tM=M)

Boundary conditions

Eigen values (R+) = resonance frequencies fQi, fSj, fTk

d2U/dz2 – A U = - (/c)2 U


Comparison measurements / model / 3d simulations

Refer to : F. Simoens, A. France, O. Delferrière, “An Equivalent 4-Wire Line Theoretical Model of Real RFQ based on the Spectral Differential Theory”, CEA-SACLAY, LINAC Conference (Gyungju, Korea), August 2002

3

2

4

L

1

C

1

L

2

L

3C

3L

4C

4

ModelMeasurements 3d simulations

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

0,0 0,5 1,0 1,5 2,0

vQ6 "2+2"

1 2 1 2

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

0,0 0,5 1,0 1,5 2,0

vQ5 "2-2"

1 2 1 2-

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

0,0 0,5 1,0 1,5 2,0

uQ "2-2"

1 2 1 2-

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

0,0 0,5 1,0 1,5 2,0

uQ "2+2"

1 2 1 2

+

-1,0

-0,5

0,0

0,5

1,0

0 500 1000 1500 2000

Hz

1 2 1 2-

-1,0

-0,5

0,0

0,5

1,0

0 500 1000 1500 2000

Hz

1 2 1 2

+


Slug tuners : fast simultaneous convergence

86 000

88 000

90 000

92 000

94 000

96 000

98 000

100 000

102 000

0,0 0,5 1,0 1,5 2,0

IPHI Vp

0

uQ(z) [u.a.]

-15

-10

-5

0

5

10

15

0 0,5 1 1,5 2

0

uT(z) [u.a.]

-15

-10

-5

0

5

10

15

0 0,5 1 1,5 2

0

uS(z) [u.a.]

fQ

0 350,62 MHz

86 000

88 000

90 000

92 000

94 000

96 000

98 000

100 000

102 000

0,0 0,5 1,0 1,5 2,0

1

-15

-10

-5

0

5

10

15

0 0,5 1 1,5 2

1

-15

-10

-5

0

5

10

15

0 0,5 1 1,5 2

1

1 352,18 MHz

86 000

88 000

90 000

92 000

94 000

96 000

98 000

100 000

102 000

0,0 0,5 1,0 1,5 2,0

2

-15

-10

-5

0

5

10

15

0 0,5 1 1,5 2

2

-15

-10

-5

0

5

10

15

0 0,5 1 1,5 2

2

2 352,22 MHz

"A " "B"

RFQ 2x1m

-0,2.10-2<(uQ-Vp)/Vp<0,2.10-2

-0,4.10-2<uD/uQ<0,4.10-2-6,4.10-2<(uQ-Vp)/Vp<3,4.10-2

-9,2.10-2<uD/uQ<10,6.10-2

Ref: F. Simoens, A. France, J. Gaiffier, “A New RFQ Model applied to the Longitudinal Tuning of a Segmented, Inhomogeneous RFQ with Highly Irregularly Spaced Tuners”, EPAC2002 Conference (Paris), June 2002


Dipole rods length adjustment

Refer to :F. Simoens, A. France, “Tuning procedure of the 5 MeV IPHI RFQ”, CEA-SACLAY, LINAC Conference (Gyungju, Korea), August 2002

Good correspondence between the measured and the ‘ideal’ dipole mode frequencies

Matching of the equivalent end loads

A new tuning criteria : ‘quadratic shift frequency’

SegmnSegmn nnffndf 22

When df(n)real RFQ df(n)ideal RFQ

0,0

0,5

1,0

1,5

2,0

2,5

0,0 0,5 1,0 1,5 2,0z [m]

U4

U2

U1U3

steep slopes

before dipole rods tuning

0,0

0,5

1,0

1,5

2,0

2,5

0,0 0,5 1,0 1,5 2,0z [m]

U1

U4

U2

U3

straightened slopes

after dipole rods tuningVoltage profiles of the first dipole mode


End plate thickness adjustment


= L x f [m.MHz] L = RFQ half-length

f = (mismatched resonance freq.) - (nominal cut-off freq.)

End region mismatch characterization : parameter

0,05

m.M

Hz

< 1

0 m

m

0,33

m.M

Hz

<

20

mm

-0,2

4 m

.MH

z

5

< 0

mm

z

v an e

end-

plat

e

Nominal mid-position thickness 0 m.MHz

Example of the IPHI RFQ cold-model end region

adjustment range [-0,24 m.MHz , +0,33 m.MHz]


End plate thickness adjustment


Parameter extraction from measurements

#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12

End #2End #1

Spectral analysis

Slugs are moved at some distance of the end being tunedi.e. for end#1, in planes #6, 7 and 8 of segment #1 = set of different voltage excitations

end#1 plate thickness

Average [m.MHz]

Std. Dev. [m.MHz]

0 -0.120 0.032

10 0.001 0.055

20 +0.300 0.086

The nominal plate thickness is well-adjusted,


ConclusionLast results

• The agreement between measurements, 3d simulations and our model validates our mathematical formalism.

• The tuning procedures of the different mechanical devices have been developed and experimentally validated.– In a 2-m long RFQ, we have achieved relative voltage error lower

than 10-2 within 3 steps of slug tuners displacements.– For the dipole rods adjustments, a new practical tuning criteria has

been introduced, that ensures the convergence of tuning.– The end region mismatch can be characterized from a set different

voltage excitations and directly related to the end plate thickness.

Studies in progress• Chronology of the different tuning procedures in the context of

the RFQ machining and assembling steps.• RF power coupling (iris / loop).

RFQ Tuning Method last results

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