Einleitung - CERN Teaching Materials

By Alicia Jones,2014-06-12 13:41
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Einleitung - CERN Teaching Materials

Fine Beam Tube


    A fine beam tube consists of a spherical glass plunger filled with noble gas under low pressure. An electron gun inside the tube (cathode, control grid and anode) generates a beam of electrons. The beam stimulates gas molecules to the emission of light, whereby the beam becomes visible within the tube. The magnetic field of two Helmholtz coils forces the electrons onto a circular path that allows us to determine the specific echarge /. m

Functional principle

     The source of the electron beam is the electron gun, which produces a stream of electrons through

    thermionic emission at the heated cathode and focuses it into a thin beam by the control grid (or

    “Wehnelt cylinder”).

     A strong electric field between cathode and anode accelerates the electrons, before they leave the

    electron gun through a small hole in the anode.

     The fine beam tube contains hydrogen molecules at low pressure, which through collisions with

    electrons are caused to emit light. This makes the orbit of the electrons indirectly visible

    e To demonstrate deflection in magnetic fields and calculate the specific charge / the fine beam tube m

    is placed in a magnetic field of two Helmholtz coils.

    Magnetic field


    Electron gun Anode U A

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Fine Beam Tube


    Equipment Assembling the experiment

    1 Fine beam tube 1. Connect the 6.3-V input end of the fine beam tube to the 6.3-V

    1 Helmholtz coils with holder and outlet of the DC power supply.

    measuring device 2. Short-circuit the positive pole of the 50-V outlet of the DC 1 DC power supply 0 … 500 V power supply with the negative pole of the 500-V outlet and 1 DC power supply 0 … 20 V connect with the socket “-” of the fine beam tube (cathode).

    1 Voltmeter, DC, <= 300 V 3. Connect the socket “+” of the fine beam tube (anode) with the

    1 Ammeter, DC, <= 3 A positive pole of the 500-V outlet, the socket W (Wehnelt-

    1 Steel tape measure, 2 m cylinder) with the negative pole of the 50-V outlet.

    3 Safety connecting leads, 25 cm 4. In order to measure the acceleration potential U connect the

    3 Safety connecting leads, 50 cm voltmeter (measuring range 300 V) to the 500-V outlet.

    7 Safety connecting leads, 100 cm 5. Short the deflection plates of the fine beam tube to the anode.

    additionally recommended: 6. Connect the DC power supply and ammeter (measuring range 1 Teslameter, 1 Axial B-probe (Fig. 3 A) in series with the Helmholtz coils.

    4), 1 Multicore cable, 6-pole, 1,5 m


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Fine Beam Tube

Experimental procedure

    1. Power up the DC power supply and set acceleration potential U = 300 V. Thermionic emission starts

    after warming up for a few minutes.

    2. Optimize focusing of the electron beam by varying the voltage at the Wehnelt-cylinder from 0 … 10 V

    until it leads to a narrow, well defined beam with clear edge definition.

    3. Connect the DC power supply of the Helmholtz coils and look for current I, at which the electron

    beam is deflected into a closed orbit.

    4. Move the left slide of the measuring device so that its

    inner edge, mirror image and escape aperture of the

    electron beam come to lay on one line of sight.

    5. Set the right slide for both inside edges to have a

    distance of 8 cm.

    6. Sight the inside edge of the right slide, align it with its

    mirror image and adjust the coil current I until the electron

    beam runs tangentially along the slide edge covering the

    mirror image

    If the electron beams after leaving the anode is deflected to the wrong (left) side:

    1. disconnect both power supplies.

    2. exchange the connections at the DC power supply in order to change the polarization of the

    magnetic field.

If the electrons do not move on a closed orbit but on a

    helical curve line:

    1. Loosen the mounting bolts of both holding

    brackets (read the information manual for the

    fine beam tube).

    2. Carefully rotate the fine beam tube around its

    longitudinal axis, until the electron beam runs

    on a closed circular orbit.

    3. Fasten mounting bolts.

Safety precautions

     Don’t touch fine beam tube and cables during operation, voltages of 300 V are used

    in this experiment!

    ! Do not exert mechanical force on the tube, danger of implosions!

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    Fine Beam Tube

    Classical experiments

    1. Build up the experimental setup (see “setup”), first without Helmholtz coils and

    observe the beam inside the tube!

    2. Magnetic deflection of the electron beam can be demonstrated by

    approaching the pole of a bar magnet to the cathode ray tube.

    3. Now add the Helmholtz coils to the experimental setup and repeat 2.

    with the magnetic field of the coils! Adjust the magnetic field so that

    the orbit of the electron beam is completely inside the tube!

    e4. Determine the specific charge / of electrons! m

    eTo determine the specific charge / you measure the radius of the circular electron beam in a m

    magnetic field B. The centripetal force at the orbit is equal to the Lorentz force:

    2mvmveevB;r; reB

    The electrons were accelerated by the voltage U between anode and cathode. That’s whz we can A

    calculate the speed of the electrons via the kinetic energy:

    1e2E;mv;eUv;2U kineAA2me

    eApplying this in the first equation you get an expression for / that only contains the parameters U, mA

    B and r that can easily be measured at the fine beam tube.

    mee r;2UAeBme

    2mme2U2eeAr;2U; A222eBmeBe

    e2UA ;22mBre

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Fine Beam Tube



    1. Generate an electron beam in the fine beam tube and adjust the

    magnetic field so that the orbit is completely inside the tube!

    2. In which way does the radius of the orbit change if you increase the

    acceleration voltage U (constant magnetic field)? A

    3. Measure the radius of the orbit at a magnetic field of B=0,0015T for

    several acceleration voltages U! A

    4. Compare to theoretical values!


    1. Since Lorentz force always act vertical to the moving direction, the electrons go on a circular path.

    That means it is possible to force particle to fly an orbit with electric fields which is used at circular

    accelerations, see below.

    2. The centripetal force at the orbit is equal to the Lorentz force:

    2mv;qvB r

    mvr; qB

    If the acceleration voltage U increases, the electrons get more kinetic energy, their speed v A

    increases as well. Because of the proportionality of r and v the radius r raises, too.

    3. The higher the acceleration voltage, the bigger is the radius of the orbit (see 2.).

    mvr;4. Calculation of the theoretical values with qB

     high UA

    U low A

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Fine Beam Tube

Particle physics: circular accelerators

    With rising energy of the accelerated particles LINACs (linear accelerators, see experiment “cathode ray

    tube”) get very long and expensive. That’s why the idea of circular accelerators was born: by using magnetic

    fields to force particles into an orbit, the same accelerating unit can be used multiple times.

    The first type of circular accelerators ever built was the cyclotron. The acceleration takes places between two D-shaped electrodes (so-called Dees) by a high frequency AC voltage. A strong magnetic field all over the Dees forces the particles onto an orbit so that the acceleration between the Dees can take place multiple times. After each semicircle particles are accelerated by the electric field between the Dees.

    Like we saw in task 2, the radius of the orbit increases with higher particle speed. Since particles were accelerated in the cyclotron each semicircle, the orbit they go is a helix that’s why high energy cyclotrons

    get very large.

     Particle source DEEs

     Magnetic field Magnetic field

     Deflection electrode



     High frequency generator

    (feste Frequenz)

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Fine Beam Tube



    1. Set the acceleration voltage to U=200V. Regularize the magnetic field thus the radius of the circular A

    path is r=4 cm!

    2. Gradually increase the acceleration voltage U in steps of 25 V. Regularize the magnetic field always A

    that the radius is constant r=4 cm! Which field strength is needed every time?

    3. Compare to calculated values!


    1. see “setup”

    2. To balance the bigger radius, the magnetic field has to be increased.

    3. Since Lorentz force equals centripetal force, we can dissolve:

    em2U2mvmvm ;qvBB;; rrqre

    This experiment with the fine beam tube showed us: it is possible to keep the radius of the orbit

    constant by increasing the magnetic field synchronously to the energy of the particles. This is used in

    circular accelerators called “synchrotrons” to keep the particles on a stationary circle (oppositional to

    the helix path inside a cyclotron). The advantage of a synchrotron is that the magnetic field needs

    only be at the path and not the whole surface of the accelerator that’s why you can build up very

    big experiments, till the 27 km long Large Hadron Collider at CERN.

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Fine Beam Tube

Particle detectors: determination of impulse and charge


    1. Use a bar magnet to show that the beam in the fine beam tube consists of negative charged


    2. Choose any desired acceleration voltage between U=200...300V and regularize the magnetic field A

    thus the electron beam is inside the glass tube. Measure the radius of the electron orbit and use this

    to calculate the impulse of the particles!

    3. Compare your result to the value of the impulse which can be calculated of the acceleration voltage!


    1. Approaching the north pole of a bar magnet from behind to the fine

    beam, the field goes forwards to the observer. Since particles fly to the

    right, the “left-hand-rule” (valid for negative charged particles) says that

    there is a Lorentz force on top. Because particles in the fine beam tube

    are deflected to the top, they are charged negatively which doesn’t

    wonder because they are electrons.

    This principle is used in particle detectors as well: for deciding if the charge of a particle is negative

    or positive, you observe the trajectory within a magnetic field. At CMS detector, the trajectory is

    measured by the tracker, made of semiconductor materials.

    Silicon tracker in the middle of the CMS detector

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    Fine Beam Tube

    2. At the circular path, centripetal and Lorentz force are equal:

    2mvqvB; r


    Because the charge of the electron q=e is known and magnetic field B and radius r can be measured,

    we can calculate the impulse of the electrons.

    In particle detectors the deflection within magnetic fields is

    used to determine the impulse of particles in the same way

    as in the fine beam tube. That’s why particle detectors need

    strong magnetic fields at the CMS detectors this is a 13m

    long superconducting solenoid with a diameter of 13 m. The

    magnetic field at the maximum current of 20.000 A is about

    4 T.

    Superconducting solenoid Myon detectors

    Myon endcap


     Electromagnetic calorimeter

    Hadron calorimeter


3. Passing the acceleration voltage U in the fine beam tube, the electrons get the kinetic energy A

    12E;eU;mvp;mv;2emU. That’s why the impulse is: . kin2

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Fine Beam Tube

    Particle detectors: determination of energy with calorimeters Tasks:

    1. In which way do the electrons become visible at the fine beam tube?

    2. Why do you need to darken the room when you use the fine beam tube?


    1. At the fine beam tube, the accelerated electrons hit atoms of the filling gas and stimulate them to

    emit light.

    The same principle is used in detectors: particles which Ionizing particle

    fly through special scintillating material (e.g. zinc sulfide)

    give away their kinetic energy to the scintillator, whose

    atoms get on a higher energy level. Dropping down to the E

    initial condition, the energy difference is emitted as a

    Photon photon. This light can transformed into an electrical signal

    by the photoelectric effect.

    Ionizing particle


    Scintillator Fiber optics Scintillators made of PbWO 4

     (transparent crystal) for the EM

     calorimeter of the CMS detector

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