CEA Codes forum

Salut Didier,

In the chart section it is possible to plot the r/Q calculated for each cavity.
For some cavities, the value seems to not be correct.
If I understand correctly, r/Q is calculated with :
r/Q = Vc^2 /(ω U )

• Vc: is the calculated accelerating voltage (plot ‘voltage per cavity’).

• U is the stored energy that has to be defined by the user in ‘Section or Family -> reflected power’;

As all cavities do not operate with the same field level (i.e. the same ke of field map), the stored energy may differ from one cavity to another.
Generally the user will define the value of the stored energy according to the targeted Eacc: defined in ‘Max. Eacc’ in Section -> cavity’. But some cavities, especially at the beginning of an accelerating section, operate at a lower field. Consequently the calculated r/Q for these cavities is not correct.

A proposed solution to correct r/Q calculation without ’breaking’ the rest of the code could be :

1. Specify to the user that the stored energy has to be defined for the targeted Eaccref (at βref = βopt or βg depending on the chosen definition of Eacc) : defined in ‘Max. Eacc’ in Section -> cavity’.
   This will enable to calculate r/Qref :
   r/Qref = (Eaccref. Lacc)^2 /(ω U)
2. Then as r/Q depends on β, the calculation for cavity #ii is :
   r/Q_ii = r/Qref * (Eacc(β_ii)/Eaccref)^2
   with Eacc(β_ii)= E0 * TTF(β_ii) & E0 = Eaccref/TTF(βref)

If you agree with this,
Would it be possible to correct the calculation of r/Q in Genlinwin?
Cheers
fred

Dear Fred,

I need some more details please about following.

r/Q_ii = r/Qref * (Eacc(β_ii)/Eaccref)^2
Eacc(β_ii)= E0 * TTF(β_ii) & E0 = Eaccref/TTF(βref)

Eaccref is the nominal Eacc, but if for different raisons (limitation phase advance for example) the field applied in cavity ii, is reduced. Typicaly, I don't see here the 'Ke' parameter.

Second reamrque: what about the refleted power, should it take this new definition of r/Q into account?

Regards,

Didier

Dear Didier

yes that is the point. you do not need to use ke to get r/Qii.
Once you calculated r/Q for the reference case (r/Qref), you just need the TTF of the cavity ii, to get its r/Qii.
By applying : r/Q_ii = r/Qref * (TTF(β_ii)/TTF(βref))^2
In this way you do not have to pay attention if the cavity operates with a reduced field or not. And the stored energy (U) is only defined once by the user for the reference case (nominal field at βopt or βg )


Regarding the reflected power, yes it should take this new r/Q calculation into account.
But for me it is not a new definition it is just correcting the calculation of r/Q of cavities that operate at reduced field.

cheers

Dear Fred,

The new r/Q calculation of cavities based on your suggestions has been introduced in the new version of GenLinWin

Regards,

Didier