Beam Particle Density: Linear vs Synchrotron Beams

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Discussion Overview

The discussion centers on the differences in particle density between linear collider beams and synchrotron beams, exploring the reasons behind the disparity in the number of particles each type can carry. Participants examine practical and theoretical limits to synchrotron beam density and the implications of luminosity in collider physics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants note that linear collider beams typically carry about 10^25 particles, while synchrotron beams carry significantly fewer, usually between 10^11 and 10^14 particles.
  • One participant suggests that the need to maintain stability and focus in synchrotron beams, along with radiation losses, may limit the number of particles that can be used.
  • Another participant questions the accuracy of the 10^25 figure for linear colliders, stating that their own research indicates numbers in the range of a few times 10^10 particles per bunch for various colliders.
  • A participant challenges the feasibility of the 10^25 figure by calculating the implications of such a number, suggesting it would require an unrealistic amount of power.
  • One participant acknowledges the lack of a source for the 10^25 figure and attempts to derive particle density from luminosity figures, questioning the assumptions made in the calculations.
  • Another participant points out that linear colliders operate with pulsed beams rather than continuous beams, which affects calculations of power and particle density.
  • It is mentioned that the beam width is typically a few microns, which would significantly lower the estimated particle density for linear colliders, aligning it more closely with synchrotron densities.
  • One participant argues against using the standard power equation (P = VI) in this context, suggesting that the dynamics of the beam do not conform to circuit behavior.

Areas of Agreement / Disagreement

Participants express disagreement regarding the particle density figures for linear colliders, with some supporting the 10^25 claim while others provide counterarguments and alternative calculations. The discussion remains unresolved, with multiple competing views on the topic.

Contextual Notes

Participants highlight potential limitations in the assumptions made regarding luminosity and particle density calculations, as well as the differences between pulsed and continuous beams. The discussion reflects varying interpretations of the underlying physics without reaching a consensus.

gbz
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Linear collider beams usually carry about 10^25 particles while synchrotron beams considerably less particles, usually 10^11 to 10^14. Why is this? Are there practical (or theoretical) limits to the density of particles in a synchrotron beam? Or is it simply because sychrotron beams can achieve similar luminosities as linear colliders with much fewer particles?
 
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All I can think of is that Synchrotons have to keep the beam stable and focused against the curvature of the accelerator whereas a linear accelerator does not. That plus the radiation released from these particles as they are acceleratred around may require that less particles be used in order to get them to that velocity.
 
gbz, are you sure about the number 1025 you quoted for linear colliders? I can't find any confirmation of that. All colliders accelerate their particles in bunches. I found numbers for the LHC, the old SLC linear collider, and the proposed ILC, and in all three cases the number of particles per bunch was comparable, a few times 1010.

Anyway, a much more important number for colliders is the luminosity (particles per second per cross-sectional area) and this depends greatly on the collision geometry, i.e. how tightly you can focus the beams at the collision point.
 
gbz is posting nonsense, I'm afraid. 1025 electrons would weigh 10 milligrams and carry 1.6 megacoulombs of charge. With 3000 bunches, you would have a pound of electrons, with nearly 5 gigacoulombs of charge. The current would be 5 gigaamps, and it would take 1021 watts to power this machine. That's a million times more power than humanity produces.
 
I received the 10^25 figure from a physicist, but admittedly I don't have a source for it. I should have double-checked it before posting, my mistake.

But I arrived at a similar number from luminosity figures for linear colliders too. SLC for instance has a luminosity of about 0.002x10^33 /cm^2 sec. Assuming N2 is 1 in the luminosity equation, given the beam is hitting a stationary target, we can derive the particle density in the beam by dividing by c (~10^8). So luminosity (10^30) divided by c (10^8) would give us 10^22 per cm^2 meter --> that is 10^22 particles per cm^2 cross section and 1 meter length of beam. Is the N2 = 1 assumption incorrect? How would you derive the particle density from luminosity for a stationary target beam?

@v50: Wasn't my intention to post 'nonsense', maybe I made some miscalculation. But I'm not sure I understand your math. How do you go from 5 GAmps to 10^21 Watts?
 
Volts x Amps = Watts

The error in your calculation is that you are assuming continuous beam. Linear colliders are pulsed.
 
10^22 particles per cm^2 cross section and 1 meter length of beam.
Of course the beam is not a centimeter across! Beam width is typically a few microns, which lowers your estimate by a factor of 108, and brings it pretty much in line with synchrotrons.
 
@v50: I doubt we can use P = VI here. This is not a circuit current, there is no resistance (except for the infinitesimal resistance of free space), so P=VI can't be applied here as far as I can tell. Anyhow, what would V be here? The voltage from one end of beam to the other is zero, the charge transfer is driven by mechanical momentum, not potential difference.

@Bill K: hmm.. that makes sense. Probably the missing factor..
 

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