I Question about Penning Trap

[kelly0303]

Hello! My question is related to a cylindrical Penning trap, with 5 electrodes (eventually each one can be divided in several parts, usually 2 or 4). I want to apply a sinusoidal electric field at the center of the trap, such that a particle inside the trap (we can assume we care only about the axial direction) feels this sinusoidal field anywhere inside a $\sim \pm 1$ mm axial amplitude (the frequency of the field will be different, much smaller, than the axial field of the trap). I ran some simulations and applying voltages to some of the electrodes in a sinusoidal fashion doesn't do what I want, as the amplitude felt by the ion in the trap is different at different axial positions, basically the ion feels something of the form:

$$A(z)sin(\omega t)$$
while I need the amplitude of the external field to not change with position. Is there a way to achieve this?

Just to clarify a bit, if I were to have a laser, with the frequency I need (the frequency I need is in RF, so no laser would do this, but let's assume we would have such a laser) and send it inside the trap, the field felt by the ion would have the same amplitude in a volume much smaller than the laser wavelength (this is the idea behind the approximations made when using lasers in the optical regime applied to atoms, where the size of the atom is much smaller than the wavelength of the laser). I would like to achieve something similar in my case if possible. Thank you!

 

[member38644]

It sounds like you are trying to create a homogeneous electric field within the trap, where the amplitude of the field does not change with position. This can be achieved by properly adjusting the voltages applied to the electrodes in the trap.

One way to achieve this is by using a technique called "electrostatic modulation." This involves applying a high-frequency (RF) voltage to one of the electrodes, while simultaneously applying a lower-frequency voltage to the other electrodes. This creates a time-varying electric field that can be adjusted to have a constant amplitude at any point within the trap.

Another option is to use a combination of DC and RF voltages on the electrodes to create a quadrupole electric field, which is homogeneous in the center of the trap. This field can then be modulated with a sinusoidal RF voltage to achieve the desired effect.

In either case, it is important to carefully design and adjust the voltages applied to the electrodes to achieve the desired field within the trap. It may also be helpful to consult with a physicist or expert in Penning traps for further guidance and assistance with your specific setup.