[MAP] Is rms emittance gauge invariant?

[Kirk T McDonald]

Alex,

Phase volume is independent of gauge, because a gauge transformation is a 
canonical transformation.

This does NOT immediately imply that rms emittance is gauge invariant --  
since rms emittance is (unfortunately) not an exact measure of phase volume.

Did Alex Dragt really claim that rms emittance is gauge invariant?

--------------
A gauge transformation
A -> A + grad f
V -> V + d f / d t
leaves the fields
E = - grad V - d A / dt
B = curl A
unchanged.

But, the terms grad V, d A / d t and curl A do not appear in an rms 
emittance calculation, which involves A and V (in case we use coordinates
x
y
t
p_x = p_mech_x + q A_x
p_y = p_mech_y + q A_y
p_t = E_mech + q V

So, it appears to me that the differences in 2nd moments of these 
quantities, which form the rms emittance, do not result in the kind of 
cancellation associated with gauge invariance.

If so, it becomes rather questionable what is the physical significance of 
rms emittance when electromagnetic fields are present (as in any particle 
accelerator).

--Kirk




-----Original Message----- 
From: Alexey Burov
Sent: Monday, March 14, 2011 8:00 AM
To: map-l at lists.bnl.gov
Subject: Re: [MAP] Liouville's theorem, kinematic invariants,and dynamic 
invariants

It was already mentioned by Alex Dragt that emiitances are independent
on the gauge transformations, since they are canonical.

On 3/13/11 10:57 PM, Valeri Lebedev wrote:
> Dear All,
> I was impressed with intensity of the discussion and a large number of 
> e-mails and would like to add a few more words.
> 1. First, there is no uncertainty with choice of the vector potential in 
> the real applications. One has to keep in mind that the reason we would 
> like to know the emittances is that we want to use this beam in a collider 
> and we need to know the emittances and Twiss parameters of the beam 
> out-coming the cooling section. That means that the computed emittances 
> have to coincide with usual emittances in the regions where magnetic field 
> is zero. For obvious reason the vector potential has to be equal to zero 
> in these regions and uncertainty disappears.
> 2. For some reason a necessity to know the Twiss parameters of out-coming 
> beam was not discussed, but, I would like to note, that the knowledge of 
> Twiss parameters is the same important as knowledge of emittances if one 
> wants to prevent the emittance growth in the course of beam transfer to 
> the collider and to minimize required apertures and, consequently, 
> non-linearities in the course of beam transport and acceleration from 
> cooling section to the collider.
>
> These problems are addressed in my and Alex Bogacz paper and I cannot 
> agree that it is too complicated to be understood by a general folks. As 
> far as I understand all problems are addressed there. Otherwise we do not 
> have a correct language to discuss cooling.
>
> Valeri
>
>
> _______________________________________________
> MAP-l mailing list
> MAP-l at lists.bnl.gov
> https://lists.bnl.gov/mailman/listinfo/map-l
_______________________________________________
MAP-l mailing list
MAP-l at lists.bnl.gov
https://lists.bnl.gov/mailman/listinfo/map-l