Simulation of coupled-bunch effects with a time-variant quadrupole

[Siwei_Wang]

Dear Michael,

Recently I'm trying to do a simulation of the coupled-bunch effects with a time-variant quadrupole in the lattice. The quadrupole strength varies in a harmonic of the revolution frequency to introduce a bunch-by-bunch tune spread that aims to cure coupled-bunch instability.

My first idea was to model the quadrupole and use the "&modulate_elements" command to change the strength with time and did several studies, and found that the tune between all the bunches is the same. After some digging I realized that the "&modulate_elements" command changes the strength of the quadrupole turn-by-turn, and couldn't show the different impact between bunches.
Do you have some ideas how I could model this time-variant quadrupole which is effective bunch-by-bunch?

Many thanks,
Siwei

[michael_borland]

Siwei,

I think the MRFDF (multipole rf deflector) element should do it. You can set up rf multipoles from dipole to decapole.

--Michael

[Siwei_Wang]

Hi Michael,

Many thanks for your reply. MRFDF works for me!

Best regards,
Siwei

[Siwei_Wang]

Dear Michael,

Many thanks for your help regarding setting the MRFDF element to simulate the time-variant quadrupole. It works well for me.

During the simulation, I met another question, i.e., the unit of B2 in MRFDF is V/m2, I'm a bit curious how it is connected with the K value of the quadrupole.
My first though was that there is a difference of speed of light between V/m2 and T/m, and in this case, most of my simulation B2 is around 1e5 to 1e6 V/m2, which results in a very small K value (something around 0.01), and doesn't seem make sense.
Then I tried to set the FREQUENCY2 to 0, aiming to set the MRFDF element as a constant quadrupole to see its impact on the beam. In this case, it seems the MRFDF is turned off, however large value I set to B2, the result was the same.

Could you give me some clue how the B2 value in unit V/m2 is connected with the quadrupole K value? Many thanks.

Best regards,
Siwei

[michael_borland]

Siwei,

To connect B2 to a more familiar quantity, we can start with equation 100 and 101 in the manual. This tells us that the peak change in x' is
dx'= x*e/(m*c^2)*(2*B2)/k/pz. In an ordinary thin quadrupole, we have dx'=x*K1*L. Hence, B2 = pz*K1*L*k/2 * (m*c^2)/e. Note that pz=betaz*gamma.

The units check out: [K1*L*k] = 1/meter^2, while (m*c^2)/e = Volts.

--Michael

[Siwei_Wang]

Dear Michael,

Many thanks for your reply. Now it is clear to me!

Kind regards,
Siwei