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Modified Cos θ Coil

Modified Cos θ Coil. A new approach in Cos θ coil design to increase the uniformity of the B field. Riccardo Schmid, CIT. A Cos θ coil with fewer turns (20 vs. 40) produces a B field with a greater gradient (greater non-uniformity).

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Modified Cos θ Coil

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  1. Modified Cosθ Coil A new approach in Cosθ coil design to increase the uniformity of the B field Riccardo Schmid, CIT

  2. A Cosθ coil with fewer turns (20 vs. 40) produces a B field with a greater gradient (greater non-uniformity). It is possible to achieve greater uniformity by combining the fields of two coils with different gradients Modified Cosθ Coil mGauss Plot of Bx(x) for Cosθ coil N=20 (black) N=40 (red) turns cm Prototype geometry (R=8.75cm, L=87.5cm)

  3. The main coil consists of a 40 turn Cosθ coil with current I1. The secondary coil consists of a 8 turn Cosθ coil with 2/5 the current in the main coil, running in the opposite direction. mGauss cm + cm mGauss Plot of Bx(x) for main Cosθ coil N=40 turns Plot of Bx(x) for secondary Cosθ coil N=8 turns with current I`= -2/5 I0

  4. The main coil consists of a 40 turn Cosθ coil with current I1. The secondary coil consists of a 8 turn Cosθ coil with 2/5 the current in the main coil, running in the opposite direction. mGauss Bx(x) Black: N=40 Cosθ coil Red: N=40-8 Modified Cosθ coil cm Plot of Bx(x) for Cosθ coil N=40 in black compared tomodified Cosθcoil 40-8 turns red (main coil N=40 turns, secondary coil N=8 turns) Prototype geometry (R=8.75cm, L=87.5cm)

  5. The main coil consists of a 40 turn Cosθ coil with current I1. The secondary coil consists of a 8 turn Cosθ coil with 2/5 the current in the main coil, running in the opposite direction. cm Bx(y) Black: N=40 Cosθ coil Red: N=40-8 Modified Cosθ coil mGauss Plot of Bx(y) for Cosθ coil N=40 in black compared tomodified Cosθcoil 40-8 turns red (main coil N=40 turns, secondary coil N=8 turns) Prototype geometry (R=8.75cm, L=87.5cm)

  6. The main coil consists of a 40 turn Cosθ coil with current I1. The secondary coil consists of a 8 turn Cosθ coil with 2/5 the current in the main coil, running in the opposite direction. mGauss Bx(z) Black: N=40 Cosθ coil Red: N=40-8 Modified Cosθ coil cm Plot of Bx(z) for Cosθ coil N=40 in black compared tomodified Cosθcoil 40-8 turns red (main coil N=40 turns, secondary coil N=8 turns) Prototype geometry (R=8.75cm, L=87.5cm)

  7. Δ Δ / 2 3Δ / 2 3Δ Simple Modification • It is possible to implement a secondary Cosθ coil without modifying the structure of the basic coil. • The secondary coil will have a number of turns equal to a divisor of the number of turns of the main coil by an odd number. • No additional grooves need to be machined • The current in the secondary coil can be implemented as current “missing” from the main. If the main coil is constructed by winding a wire multiple times, the secondary coil can be implemented by subtracting windings in some of the turns.

  8. The Volume Averaged Gradient calculations of the B field inside the fiducial volume show a lower Average Gradient for the N=40-8 coil <|dBx/dx|> calculated over a grid of points inside the fiducial volume for the prototype geometry Average Gradient Magnitude for different coils: N=20 <|dBx/dx|> = 53.988 nT/m N=40 <|dBx/dx|> = 15.531 nT/m N=40-8 <|dBx/dx|> = 2.184 nT/m For N=40-8 Gradient sign changes inside the fiducial volume: N=40-8 < dBx/dx > = .668 nT/m (not magnitude of gradient) Gradient Calculations Prototype geometry (R=8.75cm, L=87.5cm)

  9. Gradient Calculations nT/m N=20 <|dBx/dx|> = 53.988 nT/m

  10. Gradient Calculations nT/m N=40 <|dBx/dx|> = 15.531 nT/m

  11. Gradient Calculations nT/m N=40-8 <|dBx/dx|> = 2.184 nT/m

  12. The End? • Modified Cosθ coil N=40-8 seems to offer a smaller gradient compared to N=40 in the region of interest (fiducial volume) • Simple implementation in existing prototypes (N=40 at Caltech) • Increase in the current necessary to drive both coils at original B field is small (<10% increase) To do: • Measurement of the field on prototype • Calculations for new geometry L/R~6.4 (current calculation L/R=10) • Possible optimization varying secondary coil current ratio (now -2/5), number of secondary coil turns (currently 8) • Monte Carlo simulation of geometric phase

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