basic accelerator theory from a great discussion in chat
Posted: 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
[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