Atmospheric-Pressure Digital Quadrupole Ion Trap

Overview

A quadrupole trap confines charged particles using an oscillating electric field rather than a static one. Four parallel electrodes grouped into two opposing pairs surround a central axis. One rod pair is driven positive while the other is driven negative, then the polarity swaps.

On its own, a static version of this field can't trap anything: Earnshaw's theorem says you can't hold a charge in stable equilibrium using electrostatic fields alone. Instead, a quadrupole creates a saddle-shaped potential, one that pushes a charge inward along one axis while pushing it outward along the perpendicular axis. By flipping the saddle's orientation fast enough, the particle feels a net inward restoring force on average, even though the instantaneous field would otherwise seem to push it away half the time. This is the same principle behind mass spectrometers and many ion-trap quantum computing platforms, but here it's scaled up and slowed down so you can watch it happen with charged macroscopic particles outside of a vacuum chamber using stroboscopic laser illumination.

Digital Quadrupole Confinement

The two animations below show the potential across a cross-section of the trap, viewed from the side so the vertical axis represents the field strength. The four circles mark the actual rod positions, colored to show which pair is high and which is low at each instant.

The first animation shows the idealized case: a smooth sinusoidal drive, where the saddle rotates continuously and passes cleanly through zero along the diagonals. This is the textbook picture of a quadrupole field.

The second animation shows what our hardware actually does. Because the high-voltage supply is digitally switched rather than analog, the rods don't ease between polarities, they snap between two extremes. Between each polarity flip, both rod pairs are briefly pulled to the same high potential rather than opposite ones. That brief shared plateau, repeated every cycle, is what produces a net DC offset on top of the oscillating field, visible here as the flat plane the mesh collapses into before the next flip.

The core trapping behavior is identical in both cases; the difference is in the details of the drive waveform. The square-wave version is closer to what you'd measure on an oscilloscope connected to our trap, while the sinusoidal version isolates the pure restoring-force physics without the switching artifacts.

Sinewave Quadrupole Potential Gradient

Squarewave Quadrupole Potential Gradient With a Positive Offset DC Field

Instead of a continuous sine wave, this trap uses a digital square-wave drive generated by switching the electrode voltages with hardware pulse-width modulation (PWM). The end electrodes remain grounded, while the four main rods are driven by a high-voltage supply that swings roughly symmetrically around ground (0 to +/-1250 V). By adjusting the relative duty cycle between the two rod pairs, we can tune the RF confinement strength ($q$), apply a DC offset (asymmetric duty), or create a resolving DC field (complementary, non-50% duty).

Electronics