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Magnet Design

Magnet Design. W. Meng 10 May 2001. Magnet Design. ----- overview. Steps in Designing a Magnet (A) Define Specifications --- B, or G ( dB/dr, d 2 B/dr 2 ), and integral parameters uniformity, tolerances, ... (B) Field Analysis ---

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Magnet Design

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  1. Magnet Design W. Meng 10 May 2001

  2. Magnet Design ----- overview Steps in Designing a Magnet (A) Define Specifications --- B, or G (dB/dr, d2B/dr2 ), and integral parameters uniformity, tolerances, ... (B) Field Analysis --- Determine ampere-turn, pole shape, steel length ... Compute analytic parameters to match (A), estimate field qualities (C) Engineering Design --- Detailed design on mechanical structure, construction techniques, conductor cooling, resistance, voltage, … estimate assembling error, cost ...

  3. Magnet Design ----- Non-linear Materials --- steel, ferrite B = o (H +M) (si) B = H + 4  M (cgs) Finite Element Programs --- Poisson Group Code (2d: A) Opera (2d: A; 3d:  or A) MAFIA (finite integration) Ansys ( or A)

  4. Magnet Design ---- Dipole Magnet B = Bo (constant) Inside Steel: H=B/(o r)0 NI=H•dl = (Bo/o) (gap/2) (Bt Bo)

  5. Magnet Design ---- Quadrupole Magnet G = dB/dr = constant B(r) = G dr = G r Inside Steel: H=B/(o r)0 NI=H•dl = B/odr = G Ro2/(2 o) = Bt Ro/(2 o) (Bt = G Ro)

  6. Magnet Design ---- Sextupole Magnet G = d2B/dr2 = constant B(r) =  (G dr) dr = G r2/2 Inside Steel: H=B/(o r)0 NI=H•dl = B/odr = G Ro3/(6 o) = Bt Ro/(6 o) (Bt = G Ro2)

  7. Magnet Design 2d Multipole Expansion of Complex Potential --- F(z) = A(x,y) + i(x,y) z = x + i y; = (z - zo)n = (x+iy)n A(x,y) = const (Flux lines) (x,y) = const (Equ pot lines) Re Im n=1 x y n=2 x2 - y2 2xy n=3 x3 -3xy2 3x2y - y3 n=4 …...

  8. Magnet Design Multipole Expansion of Complex Field --- z = x + i y; z = r (cos + i sin) B(z) = By + iBx = [bn + i an] (z/Rref)n-1n = 1, 2... D,Q... Bx = [an cos(n-1)+ bnsin(n-1)](r/Rref)n-1 By = [bn cos(n-1)+ ansin(n-1)](r/Rref)n-1 Br(r,) = [bn sin(n-1)+ ancos(n-1)](r/Rref)n-1 B(r,) = [bncos(n-1)+ ansin(n-1)](r/Rref)n-1 an = (1/)(Rref/r)n-1 Br(r,)cos(n)d (skew) bn = (1/)(Rref/r)n-1 Br(r,)sin(n)d (normal)

  9. Magnet Design ----- Edge Chamfers (to reduced 12-pole component)

  10. Magnet Design Use edge chamfers to minimize integrated b6 (12-pole) component : 21Q40 Prototype

  11. Magnet Design ---- Shimming Tools --- an example (dB/Bo)dl 1ppm Dipole correction: top/bottom plates, wedge translation (b1constant) Quad correction: pole tilt angle, tapered wedge angle (b2 r) Sextupole correction: pole chamfers, rose shim thickness (b3 r2) …… and more: azimuthal correction, surface coils fine tuning ... Z (cm) R(cm)

  12. Injection Kicker Inconel Vac Chamber Eddy Current HeatingCeramic Vac Chamber rise time constant = 200 s eddy current plot at t = 100 s

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