- #1

1Keenan

- 100

- 3

Hello,

I would need some help in calculating the derivative of the function T_el in the attached image.

I want to calculate d T_el /d yd, where yd is the variable and it appears in the term I called A_elSide. Its expression is again in the image.

Numbers you see are not important.

Just to explain what I am trying to do:

I want to calculate energy resolution of a magnetic spectrometer (which means distance between two energy point) and it can be calculated as (dT/dy)*spotsize, basically the derivative of the energy with respect to the position on the detector and multiplied by the "nominal" beam spot size.

This means I need to express the energy as a function of the beam position.

Beam position at the detector plane is yd=R*sin(theta)+(d*tg(theta)

First term (R*sin(theta)) is the y coordinate at the magnet output, second term ((d*tg(theta) ) is the additional displacement in the drift d between magnet and detector.

Kinetic energy is in the bending radius R, so doing some math I got an expression for the kinetic enexrgy, which is T_el in the picture

Expression for T_el has an element A_elSide, cotaining the position on the detector (yd), which is the variable with respect I should do the derivative.

An now I need help, I did it already 4 times and I got 4 different results...

Any help?

I would need some help in calculating the derivative of the function T_el in the attached image.

I want to calculate d T_el /d yd, where yd is the variable and it appears in the term I called A_elSide. Its expression is again in the image.

Numbers you see are not important.

Just to explain what I am trying to do:

I want to calculate energy resolution of a magnetic spectrometer (which means distance between two energy point) and it can be calculated as (dT/dy)*spotsize, basically the derivative of the energy with respect to the position on the detector and multiplied by the "nominal" beam spot size.

This means I need to express the energy as a function of the beam position.

Beam position at the detector plane is yd=R*sin(theta)+(d*tg(theta)

First term (R*sin(theta)) is the y coordinate at the magnet output, second term ((d*tg(theta) ) is the additional displacement in the drift d between magnet and detector.

Kinetic energy is in the bending radius R, so doing some math I got an expression for the kinetic enexrgy, which is T_el in the picture

Expression for T_el has an element A_elSide, cotaining the position on the detector (yd), which is the variable with respect I should do the derivative.

An now I need help, I did it already 4 times and I got 4 different results...

Any help?