| Topic: |
Science > Physics |
| User: |
"Pedro Tamirez" |
| Date: |
27 Sep 2003 10:24:34 AM |
| Object: |
Mass dependence of maximum beam energy |
Hello!
I am having a probably very trivial question: Why is it, that proton
colliders of similar radius than electron colliders can accelerate
protons to so much more energy than electrons? Where does the particle
mass come in?
electrons protons
-----------------------------------------
1 Petra 30 GeV Tevatron 2 TeV
2 LEP 200 GeV LHC 14 TeV
-----------------------------------------
In principle I think the cavities will accelerate the particles until
their momentum equals the maximum momentum allowed by the maximum
magnetic field to keep it on a circle of radius R:
p = 0.3 B R (p: momentum, B: magnetic field)
So I don't really see where the particle mass comes in. Or could it be
that synchrotron radiation wouldn't allow the electron beam to get to
higher energies? In that case, I'd see the mass dependence of the
problem. Suppose there wasn't any synchrotron radiation, would it be
possible in principle to accelerate electrons in the tevatron to up to
2 TeV?
Would be nice if somebody could either confirm or let me know the
correct answer. Thanks very much in advance!
Pedro
.
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| User: "" |
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| Title: Re: Mass dependence of maximum beam energy |
28 Sep 2003 09:47:01 PM |
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In article <11d563b8.0309270724.72c577a9@posting.google.com>, (Pedro Tamirez) writes:
Hello!
I am having a probably very trivial question: Why is it, that proton
colliders of similar radius than electron colliders can accelerate
protons to so much more energy than electrons? Where does the particle
mass come in?
electrons protons
-----------------------------------------
1 Petra 30 GeV Tevatron 2 TeV
2 LEP 200 GeV LHC 14 TeV
-----------------------------------------
In principle I think the cavities will accelerate the particles until
their momentum equals the maximum momentum allowed by the maximum
magnetic field to keep it on a circle of radius R:
p = 0.3 B R (p: momentum, B: magnetic field)
So I don't really see where the particle mass comes in. Or could it be
that synchrotron radiation wouldn't allow the electron beam to get to
higher energies?
Yes, you got it.
In that case, I'd see the mass dependence of the
problem. Suppose there wasn't any synchrotron radiation, would it be
possible in principle to accelerate electrons in the tevatron to up to
2 TeV?
Yes. of course, I didn't check issues like orbit stability etc., but
at first glance I see no show stoppers. It is the synchrotron
radiation that is the limiting factor.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
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| User: "Uncle Al" |
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| Title: Re: Mass dependence of maximum beam energy |
27 Sep 2003 11:56:31 AM |
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Pedro Tamirez wrote:
Hello!
I am having a probably very trivial question: Why is it, that proton
colliders of similar radius than electron colliders can accelerate
protons to so much more energy than electrons? Where does the particle
mass come in?
electrons protons
-----------------------------------------
1 Petra 30 GeV Tevatron 2 TeV
2 LEP 200 GeV LHC 14 TeV
-----------------------------------------
In principle I think the cavities will accelerate the particles until
their momentum equals the maximum momentum allowed by the maximum
magnetic field to keep it on a circle of radius R:
p = 0.3 B R (p: momentum, B: magnetic field)
So I don't really see where the particle mass comes in. Or could it be
that synchrotron radiation wouldn't allow the electron beam to get to
higher energies? In that case, I'd see the mass dependence of the
problem. Suppose there wasn't any synchrotron radiation, would it be
possible in principle to accelerate electrons in the tevatron to up to
2 TeV?
Would be nice if somebody could either confirm or let me know the
correct answer. Thanks very much in advance!
Synchrotron emission loss vs. gamma varies as the inverse mass cubed
and gamma squared,
http://jilawww.colorado.edu/www/sro/thesis/heinz/appB.pdf
As the proton/electron mass ratio is 1836.153, the loss factor ratio
is 6.1 billion:1 against the electron. A proton beam radiating one
watt of synchrotron radiation is beneath notice. An electron beam at
the same gamma radiating 6 gigawatts is not tolerable.
Turn off synchrotron radiation and you are in business.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
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