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Gradients Galore: Understanding Symmetric B-Field Trajectories

Explore symmetric B-field trajectories, gradient values, and frequency shifts from an old design. Analyze the impact of cancellation of large gradients on accuracy, particularly in cases of symmetry, and delve into the divergence and sensitivity of gradient components.

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Gradients Galore: Understanding Symmetric B-Field Trajectories

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  1. GRADIENTS GALORE

  2. 1) Cylindrical symmetric B field 2) Symmetric trajectories

  3. 3)

  4. Gradient values from an old design.. (The average of the magnitude is interesting because this is expected to give a more accurate picture in the case of cancellation of large gradients due to symmetry of the field. This is seen to be the case for some components of interest. However the frequency shift is proportional to the volume average of the gradient ove the measurement cell) dBx/dx =-3.333681e-10 Gauss/cm |dBx/dx|= 6.979500e-09 Gauss/cm dBy/dy= -2.873800e-07 Gauss/cm |dBy/dy|= 2.873800e-07 Gauss/cm dBz/dz= 2.878659e-07 Gauss/cm |dBz/dz| =2.878659e-07 Gauss/cm So it seems that in this case the divergence is satisfied by having ∂By/∂y , ∂Bz/∂z cancel each other, while both are much bigger than ∂Bx/∂x .

  5. T2 depends on ∂Bx/∂x,y,z , with the greatest sensitivity to ∂Bx/∂z again because of the large dimension of the cell in this direction. dBx/dz =-4.720381e-23 Gauss/cm |dBx/dz| =4.116395e-07 Gauss/cm

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