33.3 Accelerators create matter from energy  (Page 3/9)

 Page 3 / 9

In addition to the large synchrotrons that produce colliding beams of protons and antiprotons, there are other large electron-positron accelerators. The oldest of these was a straight-line or linear accelerator    , called the Stanford Linear Accelerator (SLAC), which accelerated particles up to 50 GeV as seen in [link] . Positrons created by the accelerator were brought to the same energy and collided with electrons in specially designed detectors. Linear accelerators use accelerating tubes similar to those in synchrotrons, but aligned in a straight line. This helps eliminate synchrotron radiation losses, which are particularly severe for electrons made to follow curved paths. CERN had an electron-positron collider appropriately called the Large Electron-Positron Collider (LEP), which accelerated particles to 100 GeV and created a collision energy of 200 GeV. It was 8.5 km in diameter, while the SLAC machine was 3.2 km long.

Calculating the voltage needed by the accelerator between accelerating tubes

A linear accelerator designed to produce a beam of 800-MeV protons has 2000 accelerating tubes. What average voltage must be applied between tubes (such as in the gaps in [link] ) to achieve the desired energy?

Strategy

The energy given to the proton in each gap between tubes is ${\text{PE}}_{\text{elec}}=\text{qV}$ where $q$ is the proton’s charge and $V$ is the potential difference (voltage) across the gap. Since $q={q}_{e}=1.6×{\text{10}}^{-19}\phantom{\rule{0.25em}{0ex}}\text{C}$ and $\text{1 eV}=\left(\text{1 V}\right)\left(1.6×{\text{10}}^{-\text{19}}\phantom{\rule{0.25em}{0ex}}\text{C}\right)$ , the proton gains 1 eV in energy for each volt across the gap that it passes through. The AC voltage applied to the tubes is timed so that it adds to the energy in each gap. The effective voltage is the sum of the gap voltages and equals 800 MV to give each proton an energy of 800 MeV.

Solution

There are 2000 gaps and the sum of the voltages across them is 800 MV; thus,

${V}_{\text{gap}}=\frac{\text{800 MV}}{\text{2000}}=\text{400 kV}.$

Discussion

A voltage of this magnitude is not difficult to achieve in a vacuum. Much larger gap voltages would be required for higher energy, such as those at the 50-GeV SLAC facility. Synchrotrons are aided by the circular path of the accelerated particles, which can orbit many times, effectively multiplying the number of accelerations by the number of orbits. This makes it possible to reach energies greater than 1 TeV.

Summary

• A variety of particle accelerators have been used to explore the nature of subatomic particles and to test predictions of particle theories.
• Modern accelerators used in particle physics are either large synchrotrons or linear accelerators.
• The use of colliding beams makes much greater energy available for the creation of particles, and collisions between matter and antimatter allow a greater range of final products.

Conceptual questions

The total energy in the beam of an accelerator is far greater than the energy of the individual beam particles. Why isn’t this total energy available to create a single extremely massive particle?

Synchrotron radiation takes energy from an accelerator beam and is related to acceleration. Why would you expect the problem to be more severe for electron accelerators than proton accelerators?

What two major limitations prevent us from building high-energy accelerators that are physically small?

Problems&Exercises

At full energy, protons in the 2.00-km-diameter Fermilab synchrotron travel at nearly the speed of light, since their energy is about 1000 times their rest mass energy.

(a) How long does it take for a proton to complete one trip around?

(b) How many times per second will it pass through the target area?

(a) $2\text{.}\text{09}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\text{s}$

(b) $4\text{.}\text{77}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{Hz}$

Suppose a ${W}^{-}$ created in a bubble chamber lives for $5\text{.}\text{00}×{\text{10}}^{-\text{25}}\phantom{\rule{0.25em}{0ex}}\text{s}.$ What distance does it move in this time if it is traveling at 0.900 c ? Since this distance is too short to make a track, the presence of the ${W}^{-}$ must be inferred from its decay products. Note that the time is longer than the given ${W}^{-}$ lifetime, which can be due to the statistical nature of decay or time dilation.

What length track does a ${\pi }^{+}$ traveling at 0.100 c leave in a bubble chamber if it is created there and lives for $2\text{.}\text{60}×{\text{10}}^{-8}\phantom{\rule{0.25em}{0ex}}\text{s}$ ? (Those moving faster or living longer may escape the detector before decaying.)

78.0 cm

The 3.20-km-long SLAC produces a beam of 50.0-GeV electrons. If there are 15,000 accelerating tubes, what average voltage must be across the gaps between them to achieve this energy?

Because of energy loss due to synchrotron radiation in the LHC at CERN, only 5.00 MeV is added to the energy of each proton during each revolution around the main ring. How many revolutions are needed to produce 7.00-TeV (7000 GeV) protons, if they are injected with an initial energy of 8.00 GeV?

$1\text{.}\text{40}×{\text{10}}^{6}$

A proton and an antiproton collide head-on, with each having a kinetic energy of 7.00 TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)

When an electron and positron collide at the SLAC facility, they each have 50.0 GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.

100 GeV

a rare fraction and adjacent contraction of a sound wave are travelling in air and are separated by distance of 15cm, taken that velocity sound is 330ms what is the frequency?
Abbas
yes pls
Jennifer
Is ans 64/3
yuvraaj
2200hertz
what is speed and velocity
speed is scaler quantity and velocity is vector quantity speed has only magnitude and velocity has magnitude+direction both speed and velocity has same unit m/s
shubham
I am finding it hard to draw the velocity time graph, please can anyone assist me to know how to draw it, please?
bona
explain and draw how to measure length when using ruler, micrometer screw gauge and vernnier calliper
Calculate the average velocity in time interval 6sec to 12sec and determine the instantaneous velocity
v/6
the force is not constant in this case of tow car collide for short period of time ..why is the force is not constant?
hmmm
Fortune
calculate the average velocity in time interval 6sec to 12sec ad determine the instantaneous velocity
Lekiisi
meaning of the term si units
what what causes electric current
Chali
what what causes electric current
Chali
Charges(electron)
Caleb
Systeme international unitq@1qa@aaq
Caleb
Correct one international system of units.
Caleb
electric dynamo
albert
Electric dynamo is the sources of electric magnetic forces which utilize electromagnetic induction.
albert
A stone is dropped down a well, if it take 5 seconds to reach the water, how dip is the well
125m dip
an aircraft at as steady velocity of 70m/so eastwards at a height of 800me drops a package of supplies .a, how long will it take for the package to rich the ground? b, how fast will it be going as it lands?
what is hypothesis theory law
Tamba
144.57m/s
physics is the science of measurement
What is physics
what is physics
Obaro
Good question! Physics is the study of the nature world . Does this help?
Yonn
physics is the study of matter in relations to energy.
Enoch
physics is the science of measurements
Jide
physics is a science concern with nature and properties of matter and energy
Ugomma
what is a parallelogram law of motion?
Nancy
describe how you would find the area of an irregular shaped body?
Chali
physics is the study of natural phenomena at their most fundamental level
Yaseer
Definition for physics
It deal with matter and relation to energy
Soughie
physics is the Study of matter in relation to energy.
albert
physics is a natural science that study matter its behaviour and relation to energy.
mohammed
physic tells us more about quantities and measurement also
Kelly
life as we know it that can be measured and calculated
Jesus
what is a reference frame
what is anatomy in relation to physics
how does half life exist
The amount of time it takes a radioactive isotope to decay into a stable isotope is different for each radioactive isotope, and is characterized by its “half-life”. An isotope's half-life is the amount of time it takes for half the number of atoms of that isotope to decay to another isotope.
Nardine
what is the difference between Mass and weight
Pjustin
mass is constant while weight varies. unit of mass is kg, unit of weight is newton
Faith
how can a coin float in water and what principle governs it
in my opinion that work of surface tension but restrictions on coin is that coin do not break surface energy of molecules but some days before scientists prove that's another types of force
Aman
which force hold floating coins together thats my confusion
Aman