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MCTF

Helical Solenoid Design StudiesVladimir Kashikhin (HS), Gennady Romanov (RF)

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MCTF

Outline

• Helical Solenoid (HS) Magnetic Designs• Dielectric filled RF Cavity• HS Mechanical Design• High Pressure Vessel• Concept of HS with RF Module• Design activity directions• Summary

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MCTF Helical Solenoid Configurations (EPAC08)

• Helical Solenoids capable to generate fields required for the optimal muon cooling even at different helix periods.• Large bore straight solenoids (1), helical multipole windings (2) or trapezoidal coils (3) could be used for eliminating of the misbalance between transverse and longitudinal fields.• Demonstration models could use helical multipole windings for greater flexibility. The final design will be more efficient with non-circular shape coils. 

1 2 3

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MCTFHCC Design Study (PAC09)

Parameters of HCC sections.

ParameterUnit

Section

1st 2nd 3rd 4th

Section length  m 50 40 30 40

Helix period  m 1.00 0.80 0.60 0.40

Orbit radius  m 0.159 0.127 0.095 0.064

Solenoidal field, Bz T -6.95 -8.69 -11.6 -17.3

Helical dipole, Bt T 1.62 2.03 2.71 4.06

Helical gradient, G T/m -0.7 -1.1 -2.0 -4.5

High field helical solenoid

-80

-60

-40

-20

0

20

40

60

80

100

0 50 100 150 200 250 300

Coil Thickness (mm)

Ope

ratio

nal m

argi

n (%

)

-18.0

-15.0

-12.0

-9.0

-6.0

-3.0

0.0

3.0

6.0

Dip

ole,

Gra

dien

t (T,

T/m

)

Safety margin

Dipole

Gradient

Operation margin, helical dipole and gradient vs. coil thickness.

HS coil optimal thickness and operation margin, and SS nominal field for different HS apertures.

HS Aperture

(mm)

HS Optimal coil

thickness (mm)

HS Operation

margin (%)

SSNominal field (T)

100 200 12.9 11

120 150 -1.4 8

140 110 -17.4 6

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MCTFHybrid HS (PAC09)

Hybrid HS coil characteristics.

Layers thickness

(mm)

Normalized coil volume1

G(T/m)

Margin (%)SS

field (T)

HTS Nb3Sn HTS Total HTS Nb3Sn

200 0 1.00 1.00 -4.65 12.9 - 11.2

110 20 0.39 0.53 -4.63 11.2 18.9 11.9

100 30 0.33 0.54 -4.55 10.8 18.3 12.0

70 70 0.20 0.65 -4.13 7.7 9.3 13.5

60 90 0.16 0.75 -3.92 5.3 6.8 14.6

50 110 0.13 0.84 -3.59 2.6 3.1 16.01 the HTS coil volume and the total volume of HTS and Nb3Sn coils

normalized by the coil volume without grading

The results of coil and field optimization for a hybrid HS with an external straight solenoid (SS) are summarized in Table. The first row represents the reference HS made of HTS. In all cases Bz=‑17.3 T and Bt=4.06 T.The HTS-Nb3Sn hybrid HS provided practically the nominal value of field gradient G and the HTS coil volume reduction by a factor of 3 and the total coil volume reduction by a factor of 2. However, in this case the operation margin reduces by 16% and the nominal field of the straight solenoid increases by 7%.

However, better performance at low fields and lower cost of Nb3Sn strands with respect to HTS materials motivates using a hybrid approach and conductor grading which allows reducing the HTS coil and the total coil volume.

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MCTFHS and Beam Matching (EPAC08)

• HS with helical matching sections of 3 m long at front and far ends.

• HS design could be used in combination with tangential muon beam injection to the helical orbit. This magnet system will be cheaper for short HS channels.

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MCTFHS Magnetic Concept for MANX (PAC07)

• The solenoid consists of a number of ring coils shifted in the transverse plane such that the coil centers follow the helical beam orbit. • HS with RF has the same curent in each coil.• The current in the coils could be chaned along the HS to obtain the longitudinal field gradients.• The magnet system has a fixed relation between all components for a given set of geometrical constraints. • Thus, to obtain the necessary cooling effect, the coil should be optimized together with the beam parameters.

One could see that the optimum gradient for the helical solenoid is -0.8 T/m, corresponding to a period of 1.6 m.

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MCTF

250 MeV Muon Beam Tracking

• 250 MeV muon beam could be effectively transmitted through Helical Cooling Channel.

• The space between HS sections is 240 mm to provide RF power input, HS current leads, LHe cooling, GH2 absorber vessel, HS cryostat walls, etc…

• The field drops at the HS section ends compensated by applying additional turns.

• Shown parallel muon beam of 100 mm diameter at front end of HS.

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MCTF

Helical Solenoid Combined with RF Cavity

•The optimal helix period should be less or equal RF wave length (K.Yonehara, V. Balbekov PAC09).

• At 200 MHz - 800 MHz frequency range, the wave length and the helix period are in range of 1.5 m – 0.375 m.

• The 200 MHz cavity has 1.2 m diameter and it is too large to be placed inside HS.

• Possible solution is to use a dielectric loaded cavity (M.Popovic, et. al., PAC09) to reduce the RF cavity ID.

• The GH2 absorber at high pressure could be used for cavity cooling.

• Cavities powered through HS cryostat penetrations.

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MCTF

Dielectric Filled 200 MHz RF Cavity Cell

Inner HS diameter is 590 mm. 200 MHz pillbox type cavity with beam bore diameter of 150 mm is investigated. The cavity is filled with ceramic to reduce its overall diameter.

Cav

ity in

ner

diam

eter

2R

Total cavity length L including 2.5 mm walls

Bea

m b

ore

diam

eter

2r

Ceramic AL-995 with ε=9.6 and tan δ=0.0002 (Popovic et al., RF Cavities Loaded with Dielectric for

Muon Facilities, PAC09). Ceramic has inner radius ≥ r, outer radius = R and length = L-walls.

Vacuum

The walls of cavity are copper. Cavity beam apertures are closed with foils (or grids). In simulations the foil is made of copper as well.

Foil

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MCTF

Dielectric Filled 200 MHz Cavity Cell

Required frequency of 200 MHz, beam aperture of 15 cm diameter and given ceramic with ε=9.6 define transverse dimensions of the cavity. The minimal cavity diameter that can be achieved is 44 cm, while ceramic has inner radius 15 cm. The cavity is completely filled with ceramic material except beam bore. Therefore all transverse parameters are fixed. So, only cavity length and surface fields are available for optimization.

L=10 cm

E-field H-field

Field amplitudes correspond to 1 J of stored energy

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MCTF

Since the cavity is closed, electric field on axis E is almost constant at any cavitylength L as long as surface field Esurf is kept constant. Energy gain per cavity of length L according to the expression

will be as shown:

2/

2/

))(cos(),0(L

L

dzztzEqW

Energy Gain per Cavity

β= 0.9φ= 0ω = 2πf

Transit time factor is maximal at L=0.67m. But the helix design requires the cavities as short as possible. Let’s see what would be a result of segmentation of the accelerating channel intosequence of much shorter cavities.

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MCTFCavity Shunt Impedance and Q-factor

In an accelerating cavity we are really more interested in maximizing the particle energy gain per unit power dissipation. We define an effective shunt impedance of a cavity as

,1

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_ P

V

Pq

WR eff

effs

where q is a particle charge, P – dissipated power, Veff – effective

voltage that takes into account field phase and transit time factor.

The simulations shows thatthe cavity is very non-effectivefor shorter lengths. This is mostly because of high velocityof the muons (β≈0.9) and relatedtransit time factor.

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MCTF

Increasing of cavity length also has itsdownsides. Approximately at 30 cm asaturation of Eeff starts, while power losses are still linearly increasing. Secondarily, in longer cavity the lossesin ceramic dominate, making heatremoval more problematic.

Cavity Parameters vs. Length

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MCTF

Freq, MHz 200 L, cm 2

Q 1900 Rs eff, MOhm/m 0.6

Power total, MW 11.45 Emax, MV/m 18

Power wall, MW 7.33 Energy gain, MeV 0.36

RF Cavity Total Power

400 MHz dielectric loaded cavity

M.Popovic et al, PAC09

200 MHz dielectric loaded cavity

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MCTF

Independent phasing is very flexible. But 11 MW per cavity and 200 MHz operating frequency require extremely big transmission lines and couplers. Coupled cell structure 80 cm long and operating at 0-mode may help to reduce number of transmission lines and couplers to two units.

Coupled Cavity Cell Structure

Helical Solenoid

Coupled cell structure

Power coupler

Conductive outer wall

Ceramic filling

Conductive grid, supported by ceramic disks

Cell length 2 cm

No conductive walls between ceramic disks

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MCTF

Electric fieldAzimuthal magnetic field(no losses on grids)

Cavity 0-mode of Operation

Q = 4420; Rsh_eff = 3.84 MOhm;

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For L=80 cm shunt impedance is not maximal, but still high enough.

For 80 cm long cavity

77% of total power dissipations occurs in ceramic

80 cm long Cavity Parameters

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MCTF

RF Cavity Filling Time and Losses

Time constant τ = Qloaded /πf = 4420/(2 π 200[MHz]) = 3.52 μs Filling time (99%) T99 = 4.6 τ = 16.2 μs For rectangular RF pulse length of T99:

0 5 1 0 1 5 2 0 2 5 3 00 .0

0 .2

0 .4

0 .6

0 .8

1 .0

Tim e , s

Nor

mal

ized

field

ampl

itude

C a v ity re s p o n s e to a re c ta n g u la r p u ls e

T99

• RF cavity effective filling time 16.2 μs.

• Pulses Repetition rate 15 Hz.

• Total RF power 100 MW for 80 cm.

• Average power losses 24.3 kW

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MCTF

High Pressure Vessel for H2 Gas Absorber

• 1.6m long helical tube (1) mounted inside cylindrical shell (2) and supported at ends by flanges (3).• Tube thickness 58 mm.• Gas pressure 100 atm.• Peak Von Mises stress is 130 MPa for SS 316 (In agreement with ASME, II, part D code).• Maximum displacement is 0.55 mm.

1

2

3

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MCTF

• Hoop Lorentz forces intercepted by stainless steel rings around the coils

• Transverse Lorentz forces intercepted by support flanges

• Outer LHe vessel shell provide mechanical rigidity to the structure

• The peak stress is ~60 MPa

HS Mechanical Concept

The first model built and successfully tested

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MCTF

Helical Cooling Channel

• Helical Cooling Channel (HCC) is a Superconducting Helical Muon Beam Transport Solenoid (HS) integrated with RF acceleration system.

• The following steps should be performed during design studies and R&D before final systems integration and prototyping:

- Define RF outer dimensions, space for power wave guides, external power losses and cryoloads, system weight, etc… ;

- Define the High Pressure gas (absorber) vessel parameters; - HS magnetic and mechanical design; - HS manufacturing technology; - HS models tests; - HS unit design with space for RF system; - HS prototype unit fabrication and tests w/o RF; - HS fabrication and tests with RF.

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MCTF

HS+RF Cooling Channel

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Future Directions of Activity

• Design 200 MHz RF cavity integrated with Helical Solenoid.

• Design Helical Solenoid integrated with RF cavity.

• Continue HS short model fabrication and tests.

• Design a section of HCC.

• Fabricate and test section of HS.

• Fabricate and test section of RF.

• Assemble and test HCC (HS+RF) without absorber.

• Test HCC with absorber.

• Test HCC with a beam.

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MCTF

Model of HCC (Half Period)

The HCC model goals:

• Test RF helical structure parameters and performance in the helical magnetic field.

• Test Helical Solenoid performance.

• Test RF cavity power source.

• Test High Pressure GH2 system as absorber and cooler.

• On the base of these tests verify the HCC system design and integration with sub-systems.

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MCTF

Summary

• Proposed and investigated various versions of Helical Solenoids capable generate needed for muon ionization cooling fields.

• Proposed configuration of gas and dielectric filled helical RF system (HRF) integrated with Helical Solenoid.

• Shown a good transmission through sections of Helical Solenoid for 250MeV muon beam of 100 mm diameter.

• Estimated needed RF power, cavity parameters and average energy losses.

• Proposed concept of integration of RF cavity with Helical Solenoid in Helical Cooling Channel.

• Proposed the directions of activity in FY2010.

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MCTF

HS Design Studies Contributors

N. Andreev, V. Balbekov, E. Barzi,

V. Derbenev, A. Didenko, S. Kahn,

V.V. Kashikhin, M.Lamm, M. Lopes,

A.Makarov, D. Orris, M. Tartaglia,

R. Johnson, K. Yonehara, M. Yu,

G. Velev, A. Zlobin