Speaker: Lucy Martin
Abstract: In Nonlinear Integrable optics (NIO), a highly nonlinear magnet is inserted into a lattice with linear focusing (known as a T-insert), resulting in regular and bounded particle motion, where particles do not experience resonant excitation. NIO is a new and complex concept with clear advantages for intense beams in circular machines. The concept of NIO is being tested at Fermilab (IOTA) and the University of Maryland (UMER), but the natural chromaticity and dispersion of small circular accelerators make this process challenging. We performed detailed simulations to ascertain whether a simpler version of this theory, Quasi-Integrable nonlinear Optics (QIO), can be tested in a Paul trap. A Paul trap confines ions transversely with alternating gradient focusing, and so the transverse motion of particles in a Paul trap mimics the transverse motion of particles in an accelerator. In the Paul trap particles are extremely low energy and so can be lost without damaging the trap or irradiating and activating components and the number of ions stored in the trap can be varied so that space charge effects are included. The IBEX Paul trap, located at the Rutherford Appleton Laboratory, Oxfordshire (UK), has previously been used to experimentally explore the dynamics of intense beams. This talk describes the design process for a T-insert which meets the constraints of QIO, as well as the constraints imposed by the IBEX hardware. A number of T-insert lattices were tested on the IBEX trap, confirming that enough ions were confined to study QIO in the presence of space-charge forces and that it is possible to create a T-insert with sufficient precision. To verify that the T-insert lattice created within the Paul trap met the conditions for QIO, a method to measure the beta function in a Paul trap was designed and tested. These studies represent the first steps towards testing QIO and NIO in the simplified system of the Paul trap.
7 replies on “Nonlinear Integrable Optics in a Paul trap”
The potential that you show on slide 6 also has a linear term; are you implementing that as well in during the “nonlinear” period? You seem to focus only on the octupole term.
Is the potential on slide 6 the potential term in the Hamiltonian or the electric potential in the Paul trap? If it were the potential term in the Hamiltonian, the focusing and octupole appear to be skew.
Lucy, thank you for the nice talk. You are right that Paul trap may be unfamiliar device for some of us. So some basic questions.
Slide #4: regarding the applied potential, during the beam confinement time does the voltage stay uni-polar, or does it periodically change sign like in an RFQ?
If I compare slides #4 and #9, where is the drift region (#9) actually in the apparatus (#4)?
Slide #9: I want to know the size scale. 100 steps across drift corresponds to how many cm?
Slide #10: n x Pi. What “n” did you actually choose?
Slide #11: are the units of dimensions in the table m, or cm, or mm?
Now the tricky question.
I am trying to understand slide #14: The plot seems to be a delta-tune related parameter versus initial coordinates (x,y). Its a log scale, so bright orange/yellow are particles with large tune change, and purple are particles with very small tune change. Is that correct interpretation?
If so, do you have plots of other correlations, such as log[dQ] versus (x’,y’), etc?
Finally, many of us would call your “dynamic aperture” the “physical aperture”.
Maybe rather than try and write back all your answers, we will hear from you in person today.
Thanks
Shane
I think it really is a dynamic aperture (at least what I would call a dynamic aperture): the shape arises from the dynamics and not the beam pipe.
I’m pretty sure n=1 (slide 11).
If I understand correctly, the drift region is a place and not a time. So you see the voltage profile on slide 11 (only on the rods) followed by the voltage profile on slide 9.
We just focus on the octupole term for the quasi-integrable case, although we did think about including the linear term it will only lead to a tune shift, rather than the characteristic tune spread that leads to the added stability.
Hi Shane, sorry for the last-minute response!
On slide 4 the voltage periodically changes sign like an RFQ, in standard experiments the frequency we use is 1MHz.
The drift region described on slide 9 is a “drift region” in the accelerator like lattice we have creating using the potentials applied to the trap, and so isn’t physically in the apparatus anywhere, the confined ions experience this drift region in time.
Again, the drift region in the trap is in time, so I can’t give you a number in cm! its best to think of the trap as being a 2D model of an accelerator, the longitudinal axis in a real machine becomes time in the trap.
I used n = 1 for the phase advance in the end as I went for the simplest lattice I could design!
“So bright orange/yellow are particles with large tune change, and purple are particles with very small tune change.” – absolutely, that’s right. I do have plots of the other correlations somewhere as it’s from a Warp simulation so it spits all that data out, but will admit that I didn’t study them too closely.
Thanks for the reply to the question! Your interpretation is spot on, It is the dynamic aperture as in that plot there is no craping on the rods, the shape comes from the instability introduced by the nonlinearity.