Quadrupole Magnetic Design for an Electron Ion Collider

Paul Brindza

May 19, 2008

Achieving Small Crossing Angles

• Achieving small crossing angles requires a creative sharing of space inside SC quads with the nearby Ion or Electron beams

• It seems advantageous to place the smaller lower field final focus electron quads closest to the interaction point

• Realistic design considerations of SC quads drives solutions where the ions or electrons must pass through the quad force collar or cold yoke structures

Electron Quad Design Choices

• Reaching small crossing angles requires a “hole” in the SC magnet structure to pass the Ion beam

• A “traditional” Cosine 2 Θ Quad with a non- magnetic force collar near the coil has residual field along the Ion trajectory

• Due to lower fields in the Electron Quad the iron yoke/force collar can be adjacent to the coil

Ion Quad

• Cosine 2Θ type SC quad operating at 2 Kelvin due to high field and high current density

• Non magnetic force collar adjacent to coil

• Hole to pass Electron beam in cold yoke or in force collar with a magnetic shield

• Magnetic Design was performed with TOSCA

Electron Quad Ion Quad

Gradient 64 T/M 220 T/M

Integral Gradient 73.7 (T/M)M 248 (T/M)M

EFL 1.15 M 1.13 M

Diameter 5 cm. 6 cm

Coil Length 120 cm 120 cm

Pressure on Force Collar 1060 psi 6370 psi

Average Current Density 15,000 Amps/cm^2 37,000 Amps/cm^2

Amp Turns 207,000 Amp turns 2 x 10^6 Amp-turns

Operating Current 3500 Amps 6000 Amps

Max field in coil 2 T 8 T

Operating Temperature 4.5 K 2 K

Yoke Length 130 cm 130 cm

Stored Energy 6.3 KJ 434 KJ

Inductance 1 mH 24 mH

Properties of Electron and Ion Quads

Head on View of Electron QuadTosca Model

Model tipped by 19 mR

Gradient in Electron Quad64 T/m and 72 (T/M)M

Harmonics for E quad

Field in Ion pass thru hole

Field in Ion pass thru hole

The Ion Quad for the Electron Light Ion Collider

Ion Quad Considerations• High Gradient of 220 T/m , high current

density 37KA/cm^2 and 8Tesla fields require operation at or near 2 Kelvin

• This permits use of NbTi SC cable

• Conventional Cosine 2Θ magnet geometry

• LHC experience with high gradient quads will be a valuable guide for design

• Force collar pressure due to magnetic forces is 6370 psi

Cross section of quad with electron pass thru

Field magnitude in coil and force collar

Gradient of Ion quad220 T/M and Integral G.dL = 250 (T/M)M

Plot of By on 2.5 cm radius in main aperture

Field harmonics in Ion quad

Field Magnitude in cold yoke

Integral By.dL along length of electron pass thru (8,000 gauss cm)

Field in electron pass thru By component

Harmonics of By on 1.3 radius in electron pass thru

Ion Quad Peak Field Load Lineand NbTi SC Cable Short Sample Curve

SSC outer cable used for comparison

Conclusions• Lambertson type quads are feasible for

the final focus magnets for ELIC

• Locating the Electron quads closest to the crossing point allows a smaller crossing angle.

• ELIC quads require beam pass thru holes in the quad structural elements

• NbTi SC cables can be used in the ELIC quads however the Ion quads must operate at 2 kelvin