WIDEROE ACCELERATOR CONCEPT (IN A BOTTLE) Stephen, Leon, Daichi, Stefan Presented by:

Outline of Presentation Stephen Leon Daichi Stefan  Aims and goals  Wideroe Accelerator  Assumptions and Questions  Limits and Parameters  Frequency limit  Size of bottle  Maths behind Accelerator  Results using MATLAB plots

Aims and goals  Investigate a simple linear accelerator  Design the accelerator into a standard wine bottle  Design to get the highest energy particles possible

Electrons are accelerated by a high potential difference (kV) from cathode to anode. The blue diffusion given out by ‘Cathode rays’ are caused by fast moving electrons exciting the gas molecules left in the bottle or striking the glass and causing the excited molecules to decay emitting out photons of bluish wavelength. Homemade wine bottle CRT Cathode Anode Vacuum pump Wine bottle High Potential Difference - Extracted 23/01/2014

Ion source sends our charged particles towards the first electrode RF source flips the sign of the electrodes Ions are at constant velocity in drift tubes as voltage flips When Ions reach other side they are accelerated again and cycle repeats Wideroe Accelerator Swapped voltage Ions come out of source

Picture from last slide Taken from: Extracted: 23/01/2014

Aim: Design a Linear Accelerator in a Bottle  Assumptions: Bottle's length is ~ 50 cm Vacuum required ~ 1×10 − 3 torr Questions to be discovered  How much energy can we get by changing these parameters: f = frequency of RF U = Amplitude of alternating current m = mass of particles Length of drift tubes to be as small as possible

Limits and Parameters  Voltage has to be in kV range  Length of drift tubes  Cannot exceed breakdown voltage  3.0 MV/m – Air  MV/m – High quality vacuum  Frequency of RF voltage < 10MHz

Why the frequency limit?  The frequency limit can be shown by the simple RC circuit. The transient response is shown on the bottom left. What we see is τ = R*C, where τ is the ‘time constant’ of the capacitor. Due to this, it can be seen that at high frequencies the material doesn’t have enough time to fully charge to the given voltage. It can be seen that our system is like a parallel plate capacitor. Where dQ = C(v)*dV And C = (A/d) ε r ε 0 This presents another issue: The fact that our ‘d’ is increasing as we make our tube longer, this decreases the capacitance.

Size, an issue? As the length of each drift tube and the gap is increasing for every iteration along electron path. It can be seen that the structure will get very large, expensive and difficult to build, extremely fast. So what we’ve thought of is a systematic concept which basically involves instead of increasing the lengths incrementally but rather modulating the initial RF carrier to keep in phase with the accelerating electron.

Mathematics Behind the Design ➲ Constant velocity in the tube ➲ Equate the energy to solve for v.

Length of the Tube ➲ The time that the particle travel: T = Period, f = frequency

Length of the Gap ➲ This time, velocity is not constant But also...

Varying Voltage of RF generator (1) kVRF frequency = 5MHz

Varying Voltage of RF generator (2) RF frequency = 5MHz kV

Varying frequency of RF generator (1) MHz RF Amplitude = 25 kV

Varying frequency of RF generator (2) RF Amplitude = 25 kV MHz

Final Idea!

Questions