Transverse wakefield implementation

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Qin
Posts: 11
Joined: 22 Apr 2015, 07:48

Transverse wakefield implementation

Post by Qin » 16 Sep 2016, 12:56

HI Michael,
I am trying to simulate the transverse wakefield of a corrugated structure far away from axis, say 0.5 mm. I have a literature with analytical formula given in the form of
wy = wyd+(y-y0)*wyq. wx = - (x-x0)*wyq
with (x0,y0) the position of driving particle and (x,y) the position of probe particle. wyd, wxq are dipole and quadrupole fields and are a function of the beam offset from axis.

The problem is that how to implement the dipole wake to elegant. My plan is to do the trick as
wy = (wyd/y0 - wyq)*y0 + wyq*y
and use (wyd/y0 - wyq) as the wyClolum in TRWAKE element for dipole and wyq as the wyColumn for quad wake. Does this make sense?

Another problem is that do I need to set DX and DY ? Since y0, y are the distance of particles to the device centre but not to the reference particle, so it looks like I need to set DY=y0 to let elegant know the offset ?

I noticed this trick may lose accuracy when beam size is large, do you have any suggestion on simulating such case ?

Thank you so much,
Weilun

michael_borland
Posts: 1927
Joined: 19 May 2008, 09:33
Location: Argonne National Laboratory
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Re: Transverse wakefield implementation

Post by michael_borland » 16 Sep 2016, 13:14

Weilun,

You should be able to do this in a very straightforward fashion. Use separate TRWAKE elements for the dipole and quadrupole wakes. For the dipole wake, just use Wxd and Wyd. For the quadrupole wake, use Wxq and Wyq, but set DX=x0 and DY=y0. I don't think there is any need to modify the dipole wake as you propose. It will be taken care of automatically when you offset the TRWAKE elements.

--Michael

Qin
Posts: 11
Joined: 22 Apr 2015, 07:48

Re: Transverse wakefield implementation

Post by Qin » 16 Sep 2016, 14:37

HI Michael,

well, I may have misunderstood it but the wyd and wyq are not in the same unit. According the literature (SLAC-PUB 16497 Eq. 28, 34 and 36), the dipole field wyd is not normalized to beam offset while the quad field wyq is. The formulas are dedicated to a specific beam offset y0, not for on axis beam. The unit I get after including the device length is [V/C] for dipole and [V/C/m] for quad field. So directly implement this into TRWAKE may not be proper I think.

Thanks,
Weilun

michael_borland
Posts: 1927
Joined: 19 May 2008, 09:33
Location: Argonne National Laboratory
Contact:

Re: Transverse wakefield implementation

Post by michael_borland » 16 Sep 2016, 14:54

Weilun,

Ok, I may have been confused. Let's try again.

Elegant works in terms of the integrated wake, so the units should be V/C/m for the dipole wake and quadrupole wakes. The units for the monopole wake would be V/C. Let's assume we have monopole, dipole, and quadrupole transverse wake functions Wm(t), Wd(t), and Wq(t). The voltage seen by a probe particle at (xPP, yPP) for a drive particle at (xDP, yDP) is

Code: Select all

Vx = qDP*(Wm + Wd*xDP + Wq*xPP)
So I think what you are calling a dipole wake is what I call a monopole wake: it doesn't depend on the coordinates of the probe or drive particle. It would be a combination of the monopole wake for a centered device plus the dipole wake times the offset. Or, you can just use the DX and DY parameters on the dipole wake to add this term.

--Michael

Qin
Posts: 11
Joined: 22 Apr 2015, 07:48

Re: Transverse wakefield implementation

Post by Qin » 19 Sep 2016, 19:22

HI Michael,

Thanks for suggesting the monopole wake option. But, the wake I am trying to deal with actually is dependent on the coordinates of the drive particles. The [V/m] unit is because it is not normalized to transverse offset in analytical model ( since higher term in expansion cannot be ignored ). In my case, the beam offset is usually much larger than the beam size. That's why I want to use the wake function calculated using average beam offset to estimate wake for each drive particle.

Thanks,
Weilun

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