Charged particle guiding and beam splitting with auto-ponderomotive potentials on a chip

Electron and ion beams are indispensable tools in numerous fields of science and technology, ranging from radiation therapy to microscopy and lithography. Advanced beam control facilitates new functionalities. Here, we report the guiding and splitting of charged particle beams using ponderomotive forces created by the motion of charged particles through electrostatic optics printed on planar substrates. Shape and strength of the potential can be locally tailored by the lithographically produced electrodes’ layout and the applied voltages, enabling the control of charged particle beams within precisely engineered effective potentials. We demonstrate guiding of electrons and ions for a large range of energies (from 20 to 5000 eV) and masses (from 5 · 10−4 to 131 atomic mass units) as well as electron beam splitting for energies up to the keV regime as a proof-of-concept for more complex beam manipulation.

apertures serves as a source of charged particles. The final aperture with a diameter of 400 µm limits the size and the divergence of the beam. The strong fields between the tungsten needle tip and the extractor allow electron field emission 1 as well as ionization of gas molecules 2 , depending on the polarity of the applied acceleration voltage. For the ion beams, gas molecules of the desired noble gas species were let into the chamber by opening a leak valve connected to a supply line which was pumped and subsequently flushed by the desired gas. The partial pressure of the gas was in the order of 10 -6 mbar to achieve a sufficiently intense ion beam at the detector. Tips of varying sharpness and distance to extractor were used to realize particle beams of various energies.
For the electron beam splitting experiment, a scanning electron microscope (Philips XL30 SEM), which illuminated a spot (<1 µm) at the input, is used as the electron source. All components are Submitted Manuscript: Confidential 2 pre-aligned and fixed rigidly onto a 25 cm long electron-optical bench consisting of two straight ceramic rods. A picture of the setup is displayed in supplementary figure 1. The setup was placed into a vacuum chamber and the charged particles are detected with a microchannel plate (MCP) detector, which is placed 1 cm behind the S-curved guide (2.4 cm after the beam splitter). For the auto-ponderomotive guiding experiment, the measured intensity within a 1 mm wide square at point = 5.8 mm and = 0 mm on the detector is taken as the signal of the guided charged particles.

Layout of the S-curved guide
Pictures of the upper chip's front and back are shown in supplementary figure 2. The S-curved guide consists of two planar chips facing each other with a separation of 1 mm. They are fabricated by a standard printed circuit board process on FR4 substrates with electrodes made from goldplated copper. The chips have a total length of 11.3 cm and each chip consists of 84 electrodes.
The electrodes define an S-curve with a radius of curvature of K = 0.535 m, such that the output of the guide is laterally displaced by 5.8 mm with respect to its input. The electrodes have a length of 1.3 mm and are 1.4 mm wide. The gap between the electrodes is 100 µm wide. The electrode layout of one of the two chips is displayed in Fig. 2 in the main text. The other chip has the mirrored electrode layout but with opposite polarity. Both chips have countersinks for ruby balls which serve to align the chips. The depth of the countersinks and the diameter of the ruby balls are chosen such that the chips are separated by 1 mm. The S-curved guide can be fixed and aligned to the electronoptical bench with a holder.

Layout of the beam splitter
A picture of the electrode layout of one of the two chips is displayed in supplementary figure 3.
The other chip has the mirrored electrode layout but with opposite polarity. The beam splitter consists of two planar chips facing each other with a separation of 1 mm. They are fabricated by a standard printed circuit board process on FR4 substrates with electrodes made from gold-plated copper. The chips have a total length of 11.3 cm and each chip consists of 270 electrodes arranged in three rows. The electrodes have a length of 0.55 mm and the gap between the electrodes is 50 µm wide. The outer electrodes have a width of 1.4 mm, while the width of the inner electrodes changes along the splitter from 0.3 mm to 2.2 mm. Alignment and mounting of the chips are done as for the S-curved guides described above.

Derivation of the non-relativistic and auto-ponderomotive formula of the parameter
The stability parameter for a linear Paul trap (with 1 = AC cos and 2 = − 1 applied to adjacent rod electrodes) is given by = 2 ⋅2⋅ AC ⋅ 2 2 with the charge-to-mass ratio of the charged particles, the minimal electrodes' distance to the guide center, AC the amplitude of the alternating potential and the driving angular frequency 3 . To derive the expression of for autoponderomotive guides, one replaces the driving frequency with 2π ⋅ p . Here, is the velocity of the charged particles in the beam and the period length of the auto-ponderomotive structure. and is valid for non-relativistic particles ( ≪ speed of light ). The sign of has no effect on the stability, therefore we only calculate the absolute value. An extension for relativistic velocities can be derived by including length contraction of P and the Lorentz transformation of the electric field, but the resulting expression is only independent of the particle's charge and rest mass 0 in the limiting cases of relativistically slow and fast particles.

Calculating and the harmonic region of the auto-ponderomotive potential
The ponderomotive potential (also called the pseudopotential in the manuscript) is calculated as = 2 〈 F 2 〉 4 2 with 〈 F 2 〉 the time-averaged squared electric field. For auto-ponderomotive structures, 〈 F 2 〉 is calculated by the average of the electric field squared along the guide over the period length P . Compared to the ideal case of hyperbolic electrodes, the field strength of the quadrupole component is reduced by a geometric factor and is attained by a best fit from simulation. We obtain ≈ 0.61 for the guiding structure presented in Fig. 2 and Fig. 3 in the main text. Like in any harmonic approximation, the best fit is only valid close to the center. The discrepancy is less than 5% for displacements ≤ 80 µm from the guiding center and increases strongly for larger .

Derivation of the minimum value of for the S-curved guiding structure
The harmonic force of the ponderomotive potential H must compensate the centrifugal force Z to . The centrifugal force is given by the curvature K and the particle's velocity . Demanding that H ≥ Z leads to the guiding condition ≥ P ⋅√2 π⋅√ K ⋅ resulting in a minimum value of = 0.39 for a guiding structure with the geometry presented in this work, in excellent agreement with the experimentally observed min for all guided species (see Fig. 3 in the main text and the supplementary figure 4).

Miniaturization leads to higher trapping frequency
If the geometry of an auto-ponderomotive structure is scaled down by a factor of g , the period length P and electrode's distance to the centerline are reduced to P ′ = P g and ′ = g . The driving frequency 2π ⋅ p increases accordingly to ′ = ⋅ g . Since the stability parameter ∝ P 2 / 2 is independent of g , guiding is attained for the same applied voltage ratios for all scaling factors g and the trapping frequency = √8 increases to ′ = ⋅ g . Thus, an electrode layout on the micrometer scale leads to much higher trapping frequencies if operated at the same stability parameter . For example, using a guide with a period length P of 56 µm ( g~1 00) (which is straightforward to manufacture) and an electron beam with a kinetic energy of 1 kV results in a driving frequency of = 2π ⋅0.33 THz. Operating the guide at = 0.3 ( DC = 77.4 V, well below the breakdown voltage of high vacuum) leads to a trapping frequency of = 2π ⋅ 36 GHz.

Extended Data: Auto-ponderomotive guiding for electrons and noble gas ions
The supplementary figure 4 displays the result for all used noble gas ions as discussed around   Meandering electrodes on the back contact the electrodes on the front with plated through-holes (vias) resulting in spatially periodic voltages. The upper chip is placed above the lower chip such that their front sides are facing each other. Countersinks for ruby balls and holes for screws are drilled for alignment and fixation.