Super-cycles for LHC commissioning and operation

Super-cycles for LHC commissioning and operation.
Life in LHC - ruling over protons. 


Okuyalım öğrenelim köşemde bugün.
http://cdsweb.cern.ch/record/567170/files/1-3-sb.pdf


OM.
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Beam acceptance (admittance) in an accelerator

The maximum phase space area that particles can survive in an accelerator is called acceptance (admittance), or the dynamical aperture [1].


This discussion is related by the space demanded by the beam and the space provided by the accelerator [2]. Considering a perfect accelerator (without the field imperfections), the solution for the betatron oscillations,

A can be expressed in terms of x and x' as the following:

The  Courant-Snyder invariant A^2 defines an ellipse in the x-x' space. According to the analytic geometry, the general equation and the area of an ellipse are,

Accordingly, the area in the phase space (x-x') occupied by the beam can be deduced as,

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The admittance is associated with the maximum phase space area that can be accepted by the accelerator. At any point in an accelerator, the maximum beam size can be Asqrt(\beta). If the half aperture available to the beam is a(s), then somewhere there will be a minimum in a(s) / sqrt(\beta(s)).  

Then the acceptance (admittance) will be:

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[1] Accelerator Physics, S. Y. Lee
[2] An Introduction to the Physics of High Energy Accelerators, D. A. Edwards, M. J. Syphers

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OM.

Quench in a superconducting magnet...

A quench is an abnormal termination of magnet operation that occurs when part of the superconducting coil enters the normal (resistive) state. …wikipedia 
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Two types of quenches (irreversible transition to normal conductivity) can be distinguished: A "natural" quench occurs when either temperature T, magnetic field B, or current density J are raised beyond their critical values, for instance for magnet tests, while a "disturbance" quench may happen with the nominal working point below the critical parameters if local heating occurs. The main sources are: 
-conductor motion associated with friction under the influence of large Lorentz forces,
-and beam loss induced heating.
Due to the small heat capacity of the cable at 2-4 K, very little energy is needed to raise T beyond Tc (a few milli-Joules per cm^3). Filling the voids in the cable with LHe greatly enhances the overall heat capacity of the cable and hence its stability.


... A "hot spot", generated by some disturbance, will develop into a quench if normal conducting zone is longer than so-called minimum propagating  zone,






Here  is the average heat conductivity of the composite Cu/NbTi conductor,  its resistivity, J the current density and T0 the helium temperature. Typically a normal zone of more than 10 mm length will spread out while a shorter zone will shrink away. The quench propagation velocity in the adiabatic case (helium cooling neglected) is,


  


 is the average heat capacity of the cable. The computed velocities are in the order of 10-50 m/s


... Handbook of the Accelerator Physics and Engineering. Chao,Tigner 






--- OM