Field Map Cavities Errors on Ex; Ey; Ez

[comunian]

Dear Didier,
In TraceWin, it is possible to include errors in the cavity-field, from a field map, amplitude (E), expressed as a percentage.
However, in superconducting cavities, effects such as thermal deformation may also modify the relative contributions
of the electric-field components (E_x;E_y;E_z), without simply changing the overall field amplitude.
Is it possible to include this effect in the error study by introducing independent relative weights for the three components, for example
E=a_1*E_x;a_2*E_y;a_3*E_z,
with a relative normalization such as
a_1^2+a_2^2+a_3^2=1,
while retaining the existing global field-amplitude normalization through (E_0)?
In other words, the global amplitude error would still be controlled by (E_0), as it is currently,
while additional errors would modify the relative distribution among E_x; E_y; and E_z.
Best Regards,
Michele Comunian

[Didier]

Dear Michele,

At present, the error Ez is defined as E = Eo(1 + Err). Err is defined as a random value between [-Err; +Err]. I could envisage adding two parameters, Errx and Erry, to the error definition commands, but how do you think the random selection should be carried out?

Regards,

Didier

[comunian]

Dear Didier,
I understand that introducing independent relative errors on Ex, Ey, and Ez may be difficult.
A simpler possibility could be to introduce a random angle theta that modifies the transverse field components as follows:
Ex' = Ex cos(theta) - Ey sin(theta)
Ey' = Ex sin(theta) + Ey cos(theta)
Ez' = Ez
The applied field would then be:
Eapplied = (1 + Err) (Ex', Ey', Ez')
This transformation preserves the transverse field magnitude:
Ex'^2 + Ey'^2 = Ex^2 + Ey^2
and therefore also preserves the total field magnitude before applying the existing global amplitude error.
The random angle could be selected in the interval:
-theta_max <= theta <= theta_max
Would this be a reasonable and sufficiently simple implementation?
You need only to add a new error parameter theta.
Best regards,
Michele

[Didier]

Dear Michele,

I think it should be possible, provided I have a look at the current code structure. It might involve more complex development work than expected.
That said, I promise to look into it when I get back, because I’m on holiday from now until early September, so I’m afraid, but sorry, I won’t be able to do anything before then.

Regards,

Didier