Design of the PIPERADE Traps

Sarah Naimi

28.05.2013 PIPERADE collaboration meeting

PIPERADE section to be developed at MPIK

28.05.2013 PIPERADE collaboration meeting

Ideal Penning trap

Harmonic confinement in z-direction

28.05.2013 PIPERADE collaboration meeting

Real Penning trap

Cylindrical trap can reproduce quadrupolar potential in the center of the trap.

Anharmonic terms

Frequency shifts

We can design a trap with certain geometry and voltages to minimize anharmonic terms.

28.05.2013 PIPERADE collaboration meeting

Real Penning trap

We can calculate analytically the potential of an arbitrary cylindrical geometry if:-Endcap are grounded (VEC = 0V)-Endcap length is 3 times the inner radius (EC > 3 a)

28.05.2013 PIPERADE collaboration meeting

Real Penning trap

Compensated trap C4 & C6 vanish for T

Orthogonal trap ωz is independent of Uc

We can TUNE the geometry and voltages applied to the trap electrodes to minimize anharmonic terms.

Conditions:

28.05.2013 PIPERADE collaboration meeting

Trap design: machining precision

Results for the 8 cm trap (U0 = -10 V)For 16 cm trap & U0 = -100V better results are expected.

Minimization of C4 and C6:Imperfections of electric field do not cause frequency shifts.

Orthogonal trap: Changes in correction voltage do cause axial frequency shift.

28.05.2013 PIPERADE collaboration meeting

Trap electrodes & insulator material

-3.0x10-6 -2.0x10-6 -1.0x10-6 0.0-20

-10

0

10

20

z (m

m)

B/B

Magnetic susceptibility: χElectrode: Copper (-9.2 x 10-6)Insulator: Macor (-3.8 x 10-7)

Magnetization of material in magnetic field with strength HM = χ*H

28.05.2013 PIPERADE collaboration meeting

Homogeneous region-Axial 10-5 3cm

Bertram talk!

Trap electrodes & insulator material

28.05.2013 PIPERADE collaboration meeting

Trap design: dimension, material, precision

Electrodes (RE, CE, EC): Oxygen-free-Copper (OHFC, 99.99%) + 15 mm layer of silver (Ag) + 5 mm layer of gold (Au). Insulator: Macor.

28.05.2013 PIPERADE collaboration meeting

Trap tower assembly

28.05.2013 PIPERADE collaboration meeting

Trap tower assembly

Alignment precision: 20umOuter diaphragms: Ø = 4 mm Inner diaphragm: Ø = 2 mm

Vacuum sealing with the inner diaphragm

Maybe a motor to adjust the trap inclination for alignment with the magnetic field!

28.05.2013 PIPERADE collaboration meeting

FT-ICR detection

Results for the PIPERADE trap

Stefan Ulmer & Christian Roux PhD thesis

A suivre …

• Trap: 22 connections

• Injection electrodes: 2 x 10 connections

• Ejection electrodes: 2 x 10 connections

• Diaphragms: 3 x 2 connections

TOTAL: 90 connections!!!!

(All coming from one side…)

28.05.2013 PIPERADE collaboration meeting

The cables problem!!

28.05.2013 PIPERADE collaboration meeting

Real Penning trap

To obtain the potential solve the Laplace equation using the general Green’s function approach:

say

If endcaps are grounded and pot. vanish outer ends of the trap we can write the pot. as:

This solution gives results valid to better than 1 % in all electrostatic coefficients if the endcap length is 3 times the inner radius.