basic accelerator theory from a great discussion in chat

The place to discuss the LHC. Commissioning, operation, issues, events ....
Post Reply
User avatar
Xymox
Site Admin
Posts: 1022
Joined: Wed Nov 11, 2009 12:55 pm
Location: Phoenix, Az USA
Contact:

basic accelerator theory from a great discussion in chat

Post by Xymox » Sun Dec 13, 2009 11:00 pm

[12:58] <pcatom> do you guys want a bit of basic accelerator theory?
[13:00] <pcatom> the arrangement of magnets around the machine is called the lattice
[13:00] <pcatom> the dipoles are easy - they bend the beam around ...
[13:01] <pcatom> the quadrupoles are the magnets that focus the beam
[13:01] <pcatom> a quad is a magnet with 2N and 2S poles
[13:02] <pcatom> the field in a quad increases as you move further away from the centre ...
[13:03] <pcatom> but there is a catch - the field will act to bend the particle back towards the centre in one plane and away from the center in the other plane
[13:03] <ahu> hence the focusing action
[13:03] <pcatom> yep
[13:04] <pcatom> we call a quad which focuses in the horizontal plane a QF
[13:04] <pcatom> and one which focuses in the vertical plane a QD
[13:04] <pcatom> the lattice of the machine contains both QF and QD in the arcs these alternate
[13:05] <pcatom> the overall effect is focusing
[13:09] <pcatom> now imagine a proton in the machine with a small position error at a particular position. The focusing effect of the quads will make it oscillate around the perfect centre of the vacuum tube
[13:10] <pcatom> the number of oscillations in one turn of the machine is called the Q or the tune.
[13:10] <pcatom> it has an integer and a non integer part
[13:11] <pcatom> In the LHC the tunes are 64.28 and 59.31
[13:12] <Tau> That's x and y, I guess?
[13:12] <pcatom> yep
[13:12] <pcatom> the non-integer part is actually the more important part.
[13:12] <pcatom> if we had a tun of, say 64.000
[13:13] <pcatom> then when the proton had gone around the machine once it would find itself back exactly where it started
[13:13] <pcatom> with the same position error ...
[13:13] <pcatom> if this position error was caused by a defect then it would see the same defect again
[13:14] <pcatom> the defect might be an alignment problem or a magnetic error
[13:14] <pcatom> its error would therefore grow and the proton would soon be lost
[13:15] <pcatom> if the Q is 64.5 then every second trip around the machine would leave it seeing the same errors ...
[13:16] <pcatom> ...so the Q should ideally be an irrational number
[13:17] <pcatom> In this case the overall focusing of the lattice means that the particle will stay in the middle of the beam pipe - damped
[13:18] <pcatom> well we have 2 planes H and V and the tunes must be set such that in each plane the Q is not a low order ... ie not 0.5,0.25,0.125 or multiples thereof ...
[13:19] <pcatom> But also there is coupling between the planes so we have to avoid places where the combination of the 2 tunes becomes an integer ....
[13:21] <pcatom> All this means that we have to carefully arrange the strength of the quads around the machine to get a good value.
[13:22] <pcatom> But we don't have 1 proton - we have lots - and everyone is following a slightly different path
[13:22] <pcatom> so we have a tune spread
[13:23] <pcatom> and every proton has a slightly different energy ...
[13:24] <pcatom> the focusing effect of the quads will change with energy
[13:24] <Razuul> I see the log mentioning feed forward and feed back control of the tune, which suggests that you dynamically control the tune. If so what is your input/output?
[13:24] <pcatom> we measure it Razoul - with tiny kicks on the beam
[13:25] <pcatom> the change in focusing with energy is called the chromaticity
[13:26] <pcatom> basically lower energy protons will get focused too much - and higher energy ones too little
[13:27] <pcatom> we can correct this effect by using sextupole magnets
[13:28] <pcatom> anyway enough of that ... now to the optical functions and beam size
[13:30] <DCWhit2> Just is just the sort of level I like, enough to impressmy friends but
[13:31] <pcatom> have a look at this ... https://espace.cern.ch/be-dep/Lists/AXE ... L2009.aspx
[13:31] <pcatom> Hah - its hard work avoiding the maths!
[13:31] <pcatom> Ready to carry on?
[13:32] <pcatom> If you think about it the beam size will vary around the machine
[13:33] <pcatom> If you excite the beam at the frequency that corresponds to its tune it will resonate - like a tuning fork
[13:36] <pcatom> the beam size will vary all around the machine.
[13:37] <pcatom> i am talking about the transverse planes here by the way H and V
[13:40] <pcatom> The actual size of the beam at any location is given by an invariant part (a constant) and a bit that vaies due to the focusing effects
[13:40] <pcatom> the invariant part is called the emittance
[13:40] <pcatom> in a proton machine it is actually determined way back in the injector complex
[13:41] <pcatom> protons never forget .... the abuses heaped onto them and the emittance will increase each time
[13:43] <pcatom> i guess i need some maths here ...
[13:44] <pcatom> the beam size (S) at a specific location in the machine is given by the equation S^2 = Beta x Emittance
[13:44] <pcatom> the Beta is a value which is determined by the focusing around the machine
[13:45] <pcatom> there is a value in each plane .....
[13:45] <pcatom> the Beta is therefore a function which varies all around the machine ...
[13:45] <pcatom> it is measured in metres
[13:46] <pcatom> in the middle of the experiments we would like Beta to be small
[13:47] <pcatom> then the beam size will be small - and the rate of collisions will be high

[13:49] <MeMeX> Why is the emittance called an invariant while it changes?
[13:49] <pcatom> it is invariant around the circumference of the machine
[13:50] <pcatom> if you like it is a characteristic of the beam itself ....
[13:50] <MeMeX> I understand!

[13:52] <pcatom> if you have a large emittance then no amount of focussing can get around the fact that the beam will be bigger overall
[13:53] <pcatom> the Beta varies smoothly around the circumference of the machine

[13:55] <pcatom> sok - i am just not convinced that i am explaining it well enough
01[13:55] <Xymox> Ahahaha... oh yea you are...
[13:55] <mib_hw8pr> no, please continue, great job
01[13:55] <Xymox> ( prepairing injection )
[13:56] <Tau> Yes, please...
[13:56] <MeMeX> I agree!
[13:56] <pcatom> what else can i tell you ... mmm ...

[13:56] <pcatom> if you want a quadrupole to focus you et the beam get large in the plane that it will focus in
[13:57] <pcatom> so in a vertical focussing quad the beam is large vertically

[13:58] <pcatom> hmm - to make the beam very small in the experiments you need a small beta there
[13:59] <pcatom> to get this you need strong focussing magnets at either side


[14:01] <pcatom> just imagine the emittance as being the average beam size - it is not
[14:05] <pcatom> to make the beam very small in the experiments you need a small beta there o get this you need strong focusing magnets at either side
[14:06] <pcatom> and to get the focusing effect from these quads you therefore need a large beam size
[14:08] <pcatom> so the squeeze is a change in the settings of the quads of the machine to allow the beam to get very large in the final focusing quads - which then squeezed the beam down to be very small in the middle
[14:08] <pcatom> having a large beam size in these quads makes them delicate places ...
[14:09] <pcatom> i think i have finished trying to squeeze hahaa

kansas night owl
Posts: 5
Joined: Sat Dec 12, 2009 12:47 pm

Re: basic accelerator theory from a great discussion in chat

Post by kansas night owl » Mon Dec 14, 2009 1:51 am

Thank you so much for posting this! The fuzzy picture in my mind's eye just snapped into focus. Wonderful job of explaining the basics of what's happening, in terms I can grasp.

User avatar
LarryS
Posts: 100
Joined: Fri Dec 04, 2009 3:46 pm
Location: Seymour, CT, USA

Re: basic accelerator theory from a great discussion in chat

Post by LarryS » Mon Dec 14, 2009 3:00 am

An excellent job and was a much needed review for an "old retired physicist."

josch222
Posts: 78
Joined: Sat Dec 12, 2009 4:10 pm

Re: basic accelerator theory from a great discussion in chat

Post by josch222 » Mon Dec 14, 2009 9:54 am

So from an engineers POV the LHC is a very complex control loop with lots of
non-independent tuning parameters and lots of disturbances.
Now I have an idea why there was LHC@Home to simulate the behavior of the beams.

I wonder if they have to find new settings after the break, small hysteretic effects due
to warrmup and recooling come to mind.

And maybe the LHC could be used to detect geological movements.

Joerg.

Anitusar
Posts: 48
Joined: Fri Dec 11, 2009 5:26 pm

Re: basic accelerator theory from a great discussion in chat

Post by Anitusar » Mon Dec 14, 2009 2:16 pm

josch222 wrote:So from an engineers POV the LHC is a very complex control loop with lots of
non-independent tuning parameters and lots of disturbances.
Now I have an idea why there was LHC@Home to simulate the behavior of the beams.

I wonder if they have to find new settings after the break, small hysteretic effects due
to warrmup and recooling come to mind.

And maybe the LHC could be used to detect geological movements.

Joerg.
Actually they did. With LEP they had to take in account the moon (tidal movements) , the filling level of the lake, the traveling of the TGV from Geneva main station :!: etc. in order to calibrate the beam energy.

Pretty impressive stuff in my opinion

gluon
Posts: 28
Joined: Fri Dec 04, 2009 2:40 pm
Location: Lisbon, Portugal

Re: basic accelerator theory from a great discussion in chat

Post by gluon » Mon Dec 14, 2009 11:03 pm

Thanks for this wonderfully simple explanation. Now I understand the tunes!

Harbles
LHCPortal Guru
Posts: 314
Joined: Sat Nov 28, 2009 10:22 pm
Location: Mississauga, Ontario. Canada

Re: basic accelerator theory from a great discussion in chat

Post by Harbles » Tue Dec 15, 2009 3:29 am

Very Educational.
In the link that PCATOM left
https://espace.cern.ch/be-dep/Lists/AXE ... L2009.aspx
there are .PPT slides of the lectures in the "Introduction to Accelerator Physics" series (at the bottom) basically what he said in chat but expanded with pictures.

The Machine courses are more detailed but most have powerpoint or pdf slides at the bottom.

GEEK OUT!! WOOT!

User avatar
Tim Bergel
Posts: 29
Joined: Mon Nov 23, 2009 1:31 pm

Re: basic accelerator theory from a great discussion in chat

Post by Tim Bergel » Tue Dec 15, 2009 1:39 pm

Thanks for the great information - really makes it easier to understand what is going on!

Going to the "Introduction to accelerator physics" link given above I stumbled upon "Accelerators for pedestrians" (http://cdsweb.cern.ch/record/1017689/fi ... 07-014.pdf) which seems to be an amalgamated set of notes from the introduction, or something rather like it, in one 155 page PDF. The contents are:

1 Introduction
3 Basic notions of the mathematics you will need
17 Relativity, units, bending and quadrupole magnets
37 Lattices and Twiss parameters
53 Tune shifts, closed orbit, dispersion and chromaticity
69 Chromaticity, resonances and coupling
83 Longitudinal motion and RF
97 What is special about electrons?
109 Transfer lines, injection and ejection
119 Longitudinal Beam Instabilities
131 Transverse Beam Instabilities
139 Schottky Noise and Stochastic cooling.
151 Suggestions for further reading

Christmas reading for us all so we can understand what is going on in February :geek:

Post Reply