Oleg Zabluda's blog
Tuesday, July 10, 2012

All (?) cyclic particle colliders, including Tevatron, were colliding protons with antiprotons.
All (?) cyclic particle colliders, including Tevatron, were colliding protons with antiprotons.  It provides more available energy, after the law of charge conservation is satisfied (important for lower-energy colliders), and allows using same magnets for both beams.

But LHC collides protons with protons, which necessitates using 2 sets of magnets (~40% of the accelerator cost ), only cryo can be partially shared.

The reason is to increase luminosity (лучше хуже да больше), until we learn how to cheaply produce such a shitload of collimated antiprotons (2808 bunches of 115 billion protons each = 0.54 nanogram).

 or electrons with positrons, like LEP/LEP2. Ion colliders are different.

 1232 dipole magnets at €1M each = €1.232G. The cost of the whole LHC is €3.1G.

Random LHC calculations:

bunches are 27km/2808=9.6 m apart.
2*2808*115e9*mass of proton=1.1 nanogram
7 Tev / 938 MeV = 7,463 = Lorentz Factor
1.1 nanogram * 7,463*c^2 / 4.2e9 joules=0.18 tons of TNT -stored energy
27 km / 7,463 = 3.6 m (how long LHC is in proton's frame)
27km/2/pi = 4.3 km - radius in Lab or Proton's frame

The ring consists of circular sections with 8.1 Tesla dipole magnets bending and straight sections accelerating. Bending sections radius is:

7,463*(proton mass)*c/(proton charge)/8.1 Tesla =  2.9 km.

7,463^2*c^2/2.9 km=1.76e20 g (proper centripetal acceleration in proton frame)
c^2/2.9 km = 3.1e12 g (centripetal acceleration of proton in lab frame)
For comparison, it's exactly 15x of the neutron star surface - 2e11 g.

3.1e12 g*7,463*(proton mass) =7 Tev/2.9 km=3.9e-10 N (centripetal force on 1 proton in Lab frame)
3.9e-10*115e9 = 4.6kg (force on the bunch)

7,463-1=7,462(Thomas precession is 7462 complete revolutions per orbit or 7462*11245 Hz = 8.4e7 Hz)

(1 mm/16 microns)^2=3,906 (ratio of areas before/after focus at collision)
1/(2808*11245Hz) = 31.6 ns on average. See  why the min is 25 ns.

For comparison, for ground-state electron in a hydrogen atom
speed = 1/137 c
Loretz factor = 1.00002664
(c/137)^2/(bohr radius)=9e21 g (centripetal acceleration of electron in lab frame) ~= (proper centripetal acceleration in electron frame)
(electron mass)*9e21 g=8.2 e-9 kg (force on electron)

freq = 1/137^2*(electron mass)/h*c^2 = 6.6e15 Hz
1.00002664-1=2.664e-5 (Thomas precession, revolutions per orbit)
6.6e15*(1.00002664-1)=1.8e11 (Thomas precession per second, freq)

 http://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/collisions.htm
The bunch spacing in the LHC is 25 ns., however, there are bigger gaps (e.g. to allow dump kickers the time to get up etc.).

A 25 ns. beam  gives us a peak crossing rate of 40 MHz. Because of the gaps we get  an average crossing rate = number of bunches * revolution frequency = 2808 * 11245 = 31.6 MHz.

Proton-proton inelastic collision at 7 TeV is 60 mbrns: 60*e-3*10^-24m^2.
naive calculation of collision rate is

(60e-24*1e-3)/16e-6^2*115e9^2=3,099,609 collision per bunch crossing. The actual number is 19, due to geometry (115e9^2 is wrong). Apparently, only sqrt(19/((60e-24*1e-3)/16e-6^2))=285M protons out of 115G (0.3%) are actually colliding at the crossover point.

Quoting url above:

Inelastic event rate at nominal luminosity therefore 10e34*60*e-24 = 600 million/second per high luminosity experiment - around 19 inelastic events per crossing. I don't really know where 10^34 comes from.

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In a 2010 Science journal publication, NASA Ames Research Center astrobiologist Felisa Wolfe-Simon (now at LLNL)...
In a 2010 Science journal publication, NASA Ames Research Center astrobiologist Felisa Wolfe-Simon (now at LLNL) with big fanfare claimed that bacterium GFAJ-1 from alkaline Mono Lake, is capable of substituting arsenic (As) for a small percentage of its phosphorus (P) and grow. Then it was debunked.

Mono Lake is our stomping grounds. NASA Ames is "our" NASA research center. And astrobiology is my hobby. Let's see what happened and stuff.

Arsenic is chemically very close to P (right below it in the Periodic Table), so it easily gets incorporated instead of P into living organisms, but not so close as to actually work, that the reason it's so extremely toxic. Felisa grew the bacteria in the As environment "devoid of P", and observed growth. The erroneous results were most likely the due to trace contamination with P. Felissa stands by her results.

Still, GFAJ-1 bacteria is the current record-holder for As-resistance and tolerance for low-levels of P, but it did not substitute As for P.

Main structure (and DNA) of living organisms are made out of H,C,N,O,P.S. Water is not a part of the structure. It would be totally awesome to find any substitution. For example

H->Li
C->Si
N->P
O->S
P->As
S->Se

Any of that would be a huge deal, tremendously widening our known range of life. Too bad it didn't pan out, and after such a hype.

There was also an funny anecdote about how her husband was getting increasingly disturbed about her studying arsenic biochemistry, before she told him what she was working on. Classic.

You know who has no shortage of Phosphorus? The Hound of the Baskervilles!

http://en.wikipedia.org/wiki/GFAJ-1
http://en.wikipedia.org/wiki/Mono_Lake
http://en.wikipedia.org/wiki/Ames_Research_Center
http://en.wikipedia.org/wiki/GFAJ-1

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Seven Bridges of Königsberg, is a classic math problem, shown to have no solutions by Leonard Euler (1707-1783)...
Seven Bridges of Königsberg, is a classic math problem, shown to have no solutions by Leonard Euler (1707-1783) in 1735. There were some non-traditional solutions, like an Kaiser Wilhelm I ordering to build an 8th bridge and stuff.

1. Declare a war on the British and the Russians at the same time.
2. Have British Lancasters bomb the hell out of the the town at night
3. Have the Russians storm it, destroying >90% of the city,and 2 bridges
4. Have the Russians forcibly expel the entire German population.
6. Have the Russians demolish 2 more bridges, and replace with a highway.
7. Now that there are only 5 bridges and there is a solution.
8. ????
9. Profit

Sounds too far-fetched? Or impractical? Yet, that's exactly what happened. Life is stranger then fiction (because fiction has to make sense).

http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg#Present_state_of_the_bridges
http://en.wikipedia.org/wiki/Bombing_of_K%C3%B6nigsberg_in_World_War_II
http://ru.wikipedia.org/wiki/Мосты_Калининграда

via Matt Austern 