There is some information at the link below. I don't understand it,
but simply found it with a google search on 'cern dashboard tune
Modern accelerators and storage rings like the LHC use what is called "strong
focusing". That is, they use quadrupole magnets to focus the beam transversely,
keeping it well inside the apertures of the magnets so very little beam hits the
apertures -- that both loses that portion of the beam and also irradiates the
magnets (making them radioactive, and thus more difficult to repair as personnel
cannot remain near them). Such losses can also put undesirable backgrounds into
Strong focusing induces transverse oscillations into the beam, called "betatron
oscillations". As the beam goes around the ring, the individual particles in it
do not follow the centerline exactly, but oscillate around it, both vertically
and horizontally (repeatedly brought back by the quadrupole magnets, which act
as focusing lenses in optics). The "tune" of a circular accelerator like the LHC
is the number of betatron oscillations that occur during one turn around the
ring; there are separate tunes for vertical and horizontal, for both LHC beams.
The tune is determined primarily by the strengths and positions of the
quadrupole magnets that are spaced around the ring. There are resonances, and if
the non-integer part of the tune is equal to a ratio of small integers, then any
tiny perturbation at some location will build up over multiple turns as it
repeats in-phase with itself on successive turns -- this usually causes
catastrophic beam loss (resonances for ratios of large integers get washed out
by noise). But it takes many turns to grow the beam size, so such resonances can
be crossed by an accelerator that quickly moves the tune off resonance (at
higher momentum); for a storage ring they are disastrous.
On the LHC dashboard, the tune diagrams have lines at 0.25 (1/4) and 0.333
(1/3), which must be avoided (1/1 and 1/2 are off scale). The beam was off when
I looked, but these diagrams generally plot the horizontal vs vertical tune as a
point, or a series of points showing recent history (perhaps older ones fading
away). I believe the diagonal red line is a dynamic aperture, which is more
subtle, and must also be avoided.
Thanks, Tom. And I assume "Orbit Feedback" is similar. When I look
at the size of the beams (~1 mm) and knowing the distance they travel
it is a technical marvel that they can be steered to collide. But if
one beam was off - say - ~1/10 mm then the # of collisions would be
significantly reduced. How accurately do they know the concentricity
of the beams? What graph shows that? Perhaps the calculation of
luminosity takes all of that into account.
I'm not sure what you mean by "concentricity".
At collision, the LHC beams are on the order of 30 microns in diameter [#]. This
depends on the transverse emittance and the beta-star at the collision point --
the latter varies for each experiment, depending on their design and specific
operating mode. I believe they use automatic feedback to align the beams for
maximum collision rate (i.e. maximum luminosity).
[#] This is one sigma. The beams are approximately Gaussian out
to about 3 sigma, but are scraped at larger radius to remove the
tails (aka halo).
The calculation of luminosity certainly takes "all that" into account, plus a
whole lot more. They monitor it continuously. It is plotted in "Fill
Luminosity", which has a separate line for each experiment.
Note the ILC is MUCH more challenging to align the beams to collide, as their
beams are less than a micron in size at the collision point. Ditto for CLIC.
Electron machines can achieve much lower emittances due to the damping available
from synchrotron radiation. And the lower momentum of these machines permits a
I'm still seriously impressed by the focus and sweep angle control
of a CRT monitor (TV) 3 electron beams,RGB.
Furthermore, such an accelerator was affordable to the average
That's mass produced 'beam' control.
I think we could do much better than a micron.
Ken S. Tucker
What is the beta* parameter on the luminosity graph?
Beta is a Twiss parameter of a particle beam, basically measuring how strongly
focused it is. Beta has units of length, and the smaller it is the stronger the
focusing; it is a transverse variable, and for most beams (including each of the
LHC beams) there is a value for x and a value for y (z is along the beam and is
Together, beta and the transverse emittance determine the beam's size:
sigma_x = sqrt(emittance_x * beta_x)
In strong-focusing systems like the LHC, beta is primarily determined by the
strength of the quadrupole magnets: stronger magnets give stronger focusing and
reduced beta, and thus reduced size of the beam. Remember that in a collider,
the transverse sigma is in the denominator when computing luminosity, so smaller
beams are better.
The star in beta* means this is the value at the point of symmetry, which for
each experiment at the LHC is in the center of the detector.
Because of the premium on small values of beta at the collision regions, special
"low beta insertions" are put into the machine design at the collision
(detector) locations. They consist of special, high-gradient quadrupoles
arranged specifically to minimize beta at the collision point. These interrupt
the machine lattice, and it takes careful design to optimize the overall system.
The beam's emittance is essentially determined by the entire design, from the H-
source all the way to the collider ring; it is therefore difficult to reduce
(it's all too easy to increase it unintentionally, however). At the LHC,
technology limits the quadrupole gradients, and thus the achievable beta*. The
LHC pushes just about every machine parameter right to the technology limit.
There is a project to develop new technologies to improve the LHC luminosity,
and higher-gradient quadrupoles are at the top of the list.
> What is the beta* parameter on the luminosity graph?
You can email LHC with a reasonable question, and they will
either answer or direct you to a site that helps.
(they're the experts about LHC).
As I understand, the Beta is v/c , Beta* is the combined
collision energy of v/c with a beam doing -v/c.
Some authors use a relativistic Beta, and can mean the
increased energy in the 'beams' colliding.
(thats the relativity of inertial mass).
Focusing a beam is a challenge.
(I 1st learned about that using old B&W CRT's, a pin-prick
dot burns off the florescence).
Did you want details?
Ken S. Tucker
That is a different meaning of the letter beta. That is not what is meant in the
LHC dashboard -- see my other post for what it actually means.
> Beta* is the combined
> collision energy of v/c with a beam doing -v/c.
I have never seen this usage. I doubt that anybody but you has ever used it. It
is especially silly to use a star to switch a symbol from v/c to ENERGY.
Besides, we ALREADY have a symbol for this: s (well, s is the c-o-m energy squared).
The larger the beta (v/c as I used it), the more difficult it is
to focus the beams. A 2nd factor is the variation of the beta,
where the individual proton v/c's change how the beams focus
where a proton pulse is concerned. Add to that, proton proton
repulsion, in each beam individually.
You (Tom) pointed out the 1 to 3 sigma Gaussian sigma,
at the base of beam control is *velocity* control.
We are truly on the frontiers, similiar issues arise in ITER,
Ken S. Tucker