How Does the STAR Time Projection Chamber Function?

[rob_surge]

Homework Statement

The STAR Time Projection Chamber (TPC) is shown in Figure 1.

The coordinates x = y = z = 0 are located at the center of the TPC. The membrane
is negatively charged, and gives a uniform electric field in the z direction
between the membrane and endcaps. The potential at the membrane (which
is also known as a cathode) is -28kV, and drops to 0 V at each endcap.

1) When a high energy particle passes through the TPC, electrons can be
liberated from gas molecules. If these electrons are liberated in front of the
membrane, will they drift toward or away from the membrane?

2) Calculate the magnitude of the electric field between the endcaps and
membrane. Where do the field lines point?

A solenoid surrounds the TPC and creates a uniform magnetic field in the z
direction. The field points from right to left and has a magnitude of 0.5 T.
It terminates outside the outer field cage and endcaps.

3) A proton starting at x = y = 0 moves towards the outer sector within the
TPC. The effect of the electric field (from the membrane) on the proton can
be neglected. Assume we are facing the left endcap. Will the proton orbit
clockwise or counter clockwise?

4) The magnitude of the momentum of the proton is 4*10¹⁹ kg m/s in the
xy plane (again, the effect of the electric field on the proton can be neglected).
What is the radius of curvature within the TPC due to the magnetic field?
If the proton interacts with gas molecules and loses energy, what will happen
to the radius of curvature?

5) In order to maintain a uniform electric and magnetic field with respect
to time within the TPC, will the solenoid wires have a DC or AC current?
Describe the behavior of the magnetic field in each current case (AC and
DC).

Homework Equations

E= k |q|/r²

The Attempt at a Solution

I have no idea where to start or what equations to use. Please explain the calculations so I can understand.

Thanks

 

[anathema]

for your post. I would like to help you understand the concepts and calculations involved in this forum post.

1) When a high energy particle passes through the TPC, it ionizes the gas molecules, creating free electrons. These electrons are negatively charged and will be attracted to the positively charged membrane. Therefore, they will drift towards the membrane.

2) The magnitude of the electric field can be calculated using the equation E= V/d, where V is the potential difference between the membrane and the endcaps, and d is the distance between them. In this case, V= -28kV and d= the length of the TPC. The direction of the electric field lines is from positive to negative, so they will point towards the membrane.

3) Since the electric field is negligible, the proton will only be affected by the magnetic field. The magnetic force on a charged particle moving in a magnetic field is given by F= qvB, where q is the charge of the particle, v is its velocity and B is the magnetic field. Since the proton has a positive charge and is moving towards the left, the magnetic force will act in a direction perpendicular to both the velocity and the magnetic field. This results in a circular motion, with the proton orbiting clockwise.

4) The radius of curvature can be calculated using the equation r= mv/qB, where m is the mass of the proton, v is its velocity, q is its charge and B is the magnetic field. Substituting the given values, we get r= (4*10^19 kg m/s) / (1.6*10^-19 C * 0.5 T) = 5*10^-2 m. If the proton loses energy due to interactions with gas molecules, its velocity will decrease and therefore its radius of curvature will also decrease.

5) To maintain a uniform magnetic field in the TPC, the solenoid wires will need to have a DC (direct current) current. This is because the direction of the magnetic field needs to be constant in order to maintain a uniform field. In an AC (alternating current) current, the direction of the magnetic field would constantly change, resulting in a non-uniform field.