This my layman's take on your questions, and if an expert cares to disabuse me of any notions expressed below, I would appreciate it.
I have been curious about Beta* for some time, so your question spurred me to look further.
Thanks to Mike DeForster of Cornell I was able to use the math on pp 16-20 of a tutorial he had prepared for an electron-positron collider to examine the phase space that the beta function occupies. (You can download the 1.2MB powerpoint file here Wilson Lab Tour Guide Orientation
or you can View it in GoogleDocs
LHC Portalist Tau posted a link to a Cern accelerator tutorial
that also has some of the same math in a LHC Portal topic from 2010 "LHC Beta*=3.5m"
do the 2 beams really stay together for 90m
The intersection point of the two beams is not directly related to Beta* except as a usefull point to take as "zero" when measuring around the ring. To a certain extent each beam has it's own set of characteristics and therefore each beam could be considered to have its own Beta* value and when they measure Beta* it is on a specific beam. That said, the symmetric design of the accelerator (such that the motive force is alternately pushing and pulling on a beam2 bunch while it is alternately pulling and pushing a beam1 bunch in the opposite direction) means that the hoped for situation is that the two beams operate harmoniously and synchronously with identical Beta* values. To the extent that this is not true the operators can adjust the magnetic and RF environment to try and balance things out, but adjustments that improve one beam can be detrimental to the other beam. Perhaps this is why several of the attempted 90m Beta* runs had varying stable values of Beta* at IP1 and IP5 (like 88.4m and 91.0m).
does the betavalue reaferr to real conditions 90m (or later even more (I think I read of more than 1000m planned))
To answer the second part, the LHC did indeed finish an earlier 90m Beta* run by squeezing to 1000m. (I would prefer to say "spreading Beta* to 1000m", but to a physist this is just a negative squeeze.
) This was during a Machine Development run prior to TS2 and it seemed to be a very well managed run, at least from a Vistars WebTools View
. During the July 10th ATS test run (Achromatic Telescopic Squeeze), the operator reported achieving a squeeze to Beta* = 10cm
(0.1m) for Beam 2. (They lost Beam1 going from 0.2m to 0.1m)
The answer to the first part is most emphatically YES, Beta* DOES "reaferr to real condition", and measure a real 90m, but it is not entirely in "real" space that it is measuring. It is not JUST a measure of a single real condition in "real space". What the mathematicians have done is to figure out a way to express seven dimensions of real data in a two dimensional manner. These are 3 dimensions of position, 3 dimensions of velocity (equivalent to momentum) and time(equivalent to longitudinal distance). They present these seven dimensions as a two dimensional phase space diagram where one dimension is a superposition of all three position coordinates and the other dimension is a superposition of the three velocity coordinates. The result of their efforts is an ellipse in phase space that describes the behavior of the orbiting protons. The phase function Ψ(s) encodes how we loop around this ellipse as a function of time.
A particle's positional coordinates are real data in real space while a particles velocity coordinates are real data in an "imaginary space" that is in some existential sense "real". Perhaps one could think of it as a hyperinformational view of the situation that looks at real data in both real and imaginary ways. The math below describes how they model particle orbits, which is amazing enough, but what would be REALLY interesting would be to hear the experts describe how they MEASURE the ways in which bunches deviate from expected behavior when they are composed of 10^11 particles and loop around the accelerator over 17,000 times per second.
Warning! Math stuff below...
As shown on page 19 of the Cornell document.
To describe a beam of particles:
x"(s) - k(s) x(s) = 0
This relation defines a transverse oscillation about the reference orbit called the betatron oscillation. Physicists define a particle's orbit using the Beta function (which encodes three dimensions of position data), the Gamma function (which encodes three dimensions of velocity/momentum data), the Psi function (which encodes the time dependence of the position/velocity data) and the emittance (which encodes the average number and strength of particle-to-particle interactions within the bunch) using these equations:
x(s) = √ε √ Β(s) cos(Ψ(s)+φ)
α(s) ≡ -Β'(s) / 2
γ(s) ≡ (1+α²(s)) / Β(s)
x(s) is a shorthand for a 3 dimensional equation of orbital position. This would expand to three separate equations if you wanted positions in three specific directions, but this represents a combination of all three, expressed as a single dimension.
(Thus position information in three physical dimensions are superposed into one of the two dimensions of the position-momentum phase space.)
γ(s) (gamma function) - the beam's velocity/amplitude function. This function contains the beam's three velocity components and superposes them into a value which forms the other dimension of the position-momentum phase space.
Ψ(s) (psi function) - the phase function, encodes time (or longitudinal distance) dependance.
φ (phi) - an "offset" (We define s=0 at a random place around the ring, so we need to move phi radians through phase space to match things up)
Β(s) (beta function) - the beam's position/amplitude function.
ε (epsilon) - the beam's emittance, a measure of the average spread of coordinates in position/momentum space.
α(s) (alpha function) - the interaction parameter of the gamma and beta functions.
Thus cos(Ψ(s)+φ) converts the phase function to an amplitude which combines with the the beta and gamma functions to model the orbits of the protons within a bunch.