19-10-2010 - RF-cavities Acceleration is performed using...

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1 RF-cavities z Acceleration is performed using electric fields that are fed into Radio- Frequency (RF) cavities. RF cavities are basically resonators tuned to a selected frequency. z To accelerate a proton to 7 TeV, a potential of 7 TV must be provided to the beam: ¾ In circular accelerators the acceleration is done in small steps, turn after turn. ¾ At the LHC the acceleration from 450 GeV to 7 TeV lasts ~ 20 minutes, with an average energy gain of ~ 0.5 MeV on each turn . s ) ( t E G TM01 mode (transverse magnetic) standing wave cavity around the beam pipe 2 Acceleration with RF-cavities Principle: You send an electro-magnetic wave into a cavity and excite standing waves. The mode of the EM wave is in such a way that you will get an E-field along the axis of the cavity (such as the TM01 mode). TM01 = ground mode with the M agnetic field components only in the T ransverse plane, electric field components can be parallel (to the direction of motion of the counter propagating waves). This is the accelerating field that is responsible in accelerating the charged particles. There can be many of these cavities stacked together in series. However, because it is an oscillating field, you need to do 2 things: 1. You need to know just the right timing to inject the particles into the cavities. 2. You need to have the field in each cavity to NOT be at the same phase with each other. The phase difference depends on the nature of each cavity. In any case, you need to time the entry of the charged particle just right so that as it goes into the cavity, when the field is building in the right direction, – and as it leaves that cavity and goes into the next cavity, the field in that cavity should also start building in the right direction. How fast these fields have to build up depends on how fast the charged particles are moving through the cavities: at 450 GeV: f = 400.78 MHz ... see next slide at 7 TeV: f = 400.79 MHz (since the speed is only slightly larger)
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3 Buckets & Bunches Governed by the RF-cavities, operated at: f = 400 .8 MHz standing waves: O = c/f = 3e8/4e8 = 0.75 m max. # of possible buckets = (~26700 m)/ O = 35640 T = 1/f = 2.5 ns standing waves decelerating field o empty bucket by construction accelerating field Only every 10 th possible bucket can be filled o LHC collisions at 40 MHz, i.e. each 25 ns. max. # of bunches: 3564 (> 2808 ) Distance of filled buckets (= bunches) is 7.5 m. beam gaps due to kicker magnets! RMS bunch length: 11.2 cm 7.6 cm 450 GeV 7 TeV Eimer, Kübel, Behälter Bündel, Haufen ATLAS CMS ALICE (+11.25 m) LHCb beam 1 clockwise beam 2 anti-clockwise u u u u 1 1 17851 late 8911 nominal LHC started with: 2 bunches per beam 8 encounters per turn, 4 collisions (1 per exp!) RF-system 4 Longitudinal beam dynamics ' E t RF Voltage time LHC bunch spacing = 25 ns = 10 buckets ¡ 7.5 m 2.5 ns The particles are trapped in the RF voltage:
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19-10-2010 - RF-cavities Acceleration is performed using...

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