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### The CERN Accelerator Complex

With all the buzz this past week regarding the breaking of the world instantaneous luminosity record, I thought it might be interesting for our readers to get an idea of how we as physicists achieved this goal.

Namely, how do we accelerate particles?

(This may be a review for some of our veteran readers due to this older post by Regina)

# The Physics of Acceleration

Firstly, physicists rely on a principle many of us learn in our introductory physics courses, the Lorentz Force Law.  This result, from classical electromagnetism, states that a charged particle in the presence of external electric and/or magnetic fields will experience a force.  The direction and magnitude (how strong) of the force depends on the sign of the particle’s electric charge and its velocity (or direction its moving, and with what speed).

So how does this relate to accelerators?  Accelerators use radio frequency cavities to accelerate particles.  A cavity has several conductors that are hooked up to an alternating current source.  Between conductors there is empty space, but this space is spanned by a uniform electric field.  This field will accelerate a particle in a specific direction (again, depending on the sign of the particle’s electric charge).  The trick is to flip this current source such that as a charged particle goes through a succession of cavities it continues to accelerate, rather than be slowed down at various points.

A cool Java Applet that will help you visualize this acceleration process via radio frequency cavities can be found here, courtesy of CERN.

Now that’s the electric field portion of the Lorentz Force Law, what about the magnetic?  Well, magnetic fields are closed circular loops, as you get farther and farther away from their source the radii of these loops continually increases.  Whereas electric fields are straight lines that extend out to infinity (and never intersect) in all directions from their source.  This makes the physics of magnetic fields very different from that of electric fields.  We can use magnetic fields to bend the track (or path) of charged particles.  A nice demonstration of this can be found here (or any of the other thousands of hits I got for Googling “Cathode Ray Tube + YouTube”).

Imagine, if you will, a beam of light; you can focus the beam (make it smaller) by using a glass lens, you can also change the direction of the beam using a simple mirror.  Now, the LHC ring uses what are called dipole and quadropole magnets to steer and focus the beam.  If you combine the effects of these magnets you can make what is called a magnetic lens, or more broadly termed “Magnetic Optics.”  In fact, the LHC’s magnetic optics currently focus the beam to a diameter of ~90 micro-meters  (the diameter of a human hair is ~100 micro-meters, although it varies from person to person, and where on the body the hair is taken from).  However, the magnetic optics system was designed to focus the beam to a diameter of ~33 micro-meters.

In fact, the LHC uses 1232 dipole magnets, and 506 quadrupole magnets.  These magnets have  a peak magnetic field of 8.3 Tesla, or 100,000 times stronger than Earth’s magnetic field.  An example of the typical magnetic field emitted by the dipole magnets of the LHC ring is shown here [1]:

Image courtesy of CERN

The colored portions of the diagram indicate the magnetic flux, or the amount of magnetic field passing through a given area.  Whereas the arrows indicate the direction of the magnetic field.  The two circles (in blue) in the center of the diagram indicate the beam pipes for beams one and two.  Notice how the arrows (direction of the magnetic field) point in opposite directions!  This allows CERN Accelerator physicists to control two counter-rotating beams of protons in the same beam pipe (Excellent Question John Wells)!

Thus, accelerator physicists at CERN use electric fields to accelerate the LHC proton/lead-ion beams and the magnetic fields to steer and squeeze these beams (Also, these “magnetic optics” systems are responsible for “Lumi Leveling” discussed by Anna Phan earlier this week).

However, this isn’t the complete story, things like length contraction, and synchrotron radiation affect the acceleration process, and design of our accelerators.  But these are stories best left for another time.

# The Accelerator Complex

But where does this process start?  Well, to answer this let’s start off with the schematic of this system:

Image courtesy of CERN

One of our readers (thanks GP!) has given us this helpful link that visualizes the acceleration process at the LHC (however, when this video was made, the LHC was going to be operating at design specifications…but more on that later).

A proton’s journey starts in a tank of research grade hydrogen gas (impurities are measured in parts per million, or parts per billion).  We first take molecular hydrogen (a diatomic molecule for those of you keeping track) and break it down into atomic hydrogen (individual atoms).  Next, we strip hydrogen’s lone electron from the atom (0:00 in the video linked above).  We are now left with a sample of pure protons.  These protons are then passed into the LINear ACcelerator 2 (LINAC2, 0:50 in the video linked above), which is the tiny purple line in the bottom middle of the above figure.

The LINAC 2 then accelerates these protons to an energy of 50 MeV, or to a 31.4% percent of the speed of light [2].  The “M” stands for mega-, or times one million.  The “eV” stands for electron-volts, which is the conventional unit of high energy physics.  But what is an electron-volt, and how does it relate to everyday life?  Well, for that answer, Christine Nattrass has done such a good job comparing the electron-volt to a chocolate bar, that any description I could give pales in comparison to hers.

Moving right along, now thanks to special relativity, we know that as objects approach the speed of light, they “gain mass.”  This is because energy and mass are equivalent currencies in physics.  An object at rest has a specific mass, and a specific energy.  But when the object is in motion, it has a kinetic energy associated with it.  The faster the object is moving, the more kinetic energy, and thus the more mass it has.  At 31.4% the speed of light, a proton’s mass is ~1.05 times its rest mass (or the proton’s mass when it is not moving).

So this is a cruel fact of nature.  As objects increase in speed, it becomes increasingly more difficult to accelerate them further!  This is a direct result of Newton’s Second Law.  If a force is applied to a light object (one with little mass) it will accelerate very rapidly; however, the same force applied to a massive object will cause a very small acceleration.

Now at an energy of 50 MeV, travelling at 31.4% the speed of light, and with a mass of 1.05 times its rest mass, the protons are injected into the Proton Synchrotron (PS) Booster (1:07 in the video).  This is the ellipse, labeled BOOSTER, in the diagram above.  The PS Booster then accelerates the protons to an energy of 1.4 GeV (where  the “G” stands for giga- or a billion times!), and a velocity that is 91.6% the speed of light [2].  The proton’s mass is now ~2.49 times its rest mass.

The PS Booster then feeds into the Proton Synchrotron (labeled as PS above, see 2:03 in video), which was CERN’s first synchrotron (and was brought online in November of 1959).  The PS then further accelerates the protons to an energy of 25 GeV, and a velocity that is 99.93% the speed of light [2].  The proton’s mass is now ~26.73 times its rest mass!  Wait, WHAT!?

At 31.4% the speed of light, the proton’s mass has barely changed from its rest mass.  Then at 91.6% the speed of light (roughly three times the previous speed), the proton’s mass was only two and a half times its rest mass.  Now, we increased speed by barely 8%, and the proton’s mass was increase by a factor of 10!?

This comes back to the statement earlier, objects become increasingly more difficult to accelerate the faster they are moving.  But this is clearly a non-linear affect.  To get an idea of what this looks like mathematically, take a look at this link here [3].  In this plot, the Y-axis is in multiples of rest mass (or Energy), and the x-axis is velocity, in multiples of the speed of light, c.  The red line is this relativistic effect that we are seeing, as we go from ~91% to 99% the speed of light, the mass increases gigantically!

But back to the proton’s journey, the PS injects the protons into the Super Proton Synchrotron (names in high energy physics are either very generic, and bland, or very outlandish, e.g. matter can be charming).  The Super Proton Synchrotron (SPS, also labeled as such in above diagram, 3:10 in video above) came online in 1976, and it was in 1983 that the W and Z bosons (mediators of the weak nuclear force) were discovered when the SPS was colliding protons with anti-protons.  In today’s world however, the SPS accelerates protons to an energy of 450 GeV, with a velocity of 99.9998% the speed of light [2].  The mass of the proton is now ~500 times its rest mass.

The SPS then injects the proton beams directly into the Large Hadron Collider.  This occurs at 3:35 in video linked above, however, when this video was recorded the LHC was operating at design energy, with each proton having an energy of 7 TeV (“T” for tera-, a million million times).  However, presently the LHC accelerates the proton to half of the design energy, and a velocity of 99.9999964% the speed of light.  The protons are then made to collide in the heart of the detectors.  At this point the protons have a mass that is ~3730 times their rest mass!

So, the breaking of the world instantaneous luminosity record was not the result of one single instrument, but the combined might of CERN’s full accelerator complex, and in no small part by the magnetic optics systems in these accelerators (I realize I haven’t gone into much detail regarding this, my goal was simply to introduce you to the acceleration process that our beams undergo before collisions).

Until next time,

-Brian

References:

[1] CERN, “LHC Design Report,” https://ab-div.web.cern.ch/ab-div/Publications/LHC-DesignReport.html

[2] CERN, “CERN faq: The LHC Guide,” http://cdsweb.cern.ch/record/1165534/files/CERN-Brochure-2009-003-Eng.pdf

[3]  School of Physics, University of Southern Wales, Sydney Australia, http://www.phys.unsw.edu.au/einsteinlight/jw/module5_equations.htm

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