Electric Accumulation of Millicharged Particles

TL;DR

The paper demonstrates that a conducting shell charged to a high voltage can serve as an efficient accumulator for room-temperature millicharged particles, dramatically increasing their local density and enabling sensitive tests inside the shell. It analyzes two terrestrial mCP populations—the DM subcomponent and irreducible cosmic-ray–produced mCPs—and develops a quantitative model of accumulation that includes diffusion, trapping, evaporation, and environmental effects. The results show overdensities up to about 1e12 for plausible outdoor configurations, with substantial contributions from both DM- and cosmic-ray–sourced mCPs; kinetically-mixed scenarios are discussed, highlighting backreaction limits. The approach offers a complementary path to accelerator searches for sub-GeV mCPs and motivates integrating detectors like ion traps or Cavendish-type experiments inside such accumulators to probe new regions of parameter space.

Abstract

A terrestrial population of millicharged particles that interact significantly with normal matter can arise if they make up a dark matter subcomponent or if they are light enough to be produced in cosmic ray air showers. Such particles thermalize to terrestrial temperatures through repeated scatters with normal matter in Earth's environment. We show that a simple electrified shell (e.g., a Van de Graaff generator) functions as an efficient accumulator of such room-temperature millicharged particles, parametrically enhancing their local density by as much as twelve orders of magnitude. This can be used to boost the sensitivity of any detector housed in the shell's interior, such as ion traps and tests of Coulomb's law. In a companion paper, we apply this specifically to Cavendish tests of Coulomb's law, and show that a well-established setup can probe a large region of unexplored parameter space, with sensitivity to the irreducible density of millicharged particles generated from cosmic rays that outperforms future accelerator searches for sub-GeV masses.

Figures (5)

• Figure 1: A schematic of our experimental proposal. A large "accumulator shell" of radius $R_0$ is charged to strong negative voltage, $\phi_0$. This attracts positively-charged millicharged particles $\chi^+$, which lose energy after scattering on an enclosed solid sphere, and become electrically trapped within the cavity of the shell, parametrically enhancing their local density. The trajectories of various millicharged particles are shown with arrows, where the color of the arrow is meant to show regions where the particles are moving with greater (red) or smaller (blue) kinetic energy. A detector can be placed inside the shell to detect this millicharge overdensity (see Ref. forthcoming).
• Figure 2: The minimum coupling $q_\chi$ required for a millicharged particle of mass $m_\chi$ to cool down to room temperature within an Earth radius after scattering with terrestrial atoms, for various choices of the particle's initial boost times velocity $\gamma_\chi v_\chi$ ($\gamma_\chi v_\chi = 10^{-3}$ for millicharged dark matter, and $\gamma_\chi v_\chi \gtrsim 1$ for relativistic millicharged particles, such as those created by cosmic rays). In gray, we also show existing limits from accelerator probes Davidson:2000hfHaas:2014ddaPrinz:1998uaArgoNeuT:2019ckqmilliQan:2021lneArguellesDelgado:2021lekPBC:2025snyCMS:2024eyxAlcott:2025rxn and SN1987A Chang:2018rso.
• Figure 3: The terrestrial density $n_\chi$ of positively-charged millicharged particles that are produced by cosmic rays and thermalize to room temperature through scattering with Earth's environment, as a function of the particle's mass $m_\chi$ and charge $q_\chi$. In gray, we also show existing limits from accelerator probes Davidson:2000hfHaas:2014ddaPrinz:1998uaArgoNeuT:2019ckqmilliQan:2021lneArguellesDelgado:2021lekPBC:2025snyCMS:2024eyxAlcott:2025rxn and SN1987A Chang:2018rso. In the left-panel, "$E_\oplus = 0$" means we ignore the coupling of millicharged particles to the atmospheric electric field. In the right-panel, "$E_\oplus \neq 0$" means we instead assume that the millicharged particles couple to the atmospheric electric field, such that positively-charged particles can become electrically bound below the atmosphere. In both panels, we evaluate the density at a depth of $1 \ \text{m}$ below the crust (these results also apply to the density inside of a conducting building above the surface). In the left-panel, there is substantial depth-dependence to $n_\chi$, with greater densities further underground. In the right-panel, there is negligible depth-dependence below the crust.
• Figure 4: The overdensity $n_\text{trap} / n_\chi$ of millicharged particles accumulated by an electric trap (compared to the average nearby terrestrial density), as a function of the millicharge $q_\chi$ and mass $m_\chi$. The trap consists of a room-temperature shell of radius $R_0 = 2 \ \text{m}$, held at a voltage of $\phi_0 = - 1 \ \text{MV}$ for a time $t = 1 \ \text{yr}$. We consider a setup operated outdoors (left) or indoors (right). In gray, we also show existing limits from accelerator probes Davidson:2000hfHaas:2014ddaPrinz:1998uaArgoNeuT:2019ckqmilliQan:2021lneArguellesDelgado:2021lekPBC:2025snyCMS:2024eyxAlcott:2025rxn and SN1987A Chang:2018rso. The region of parameter space for which overdensities can develop is limited to a finite region of masses and couplings: at small masses, millicharged particles are less efficient at thermalizing in the shell through scattering, and at large masses Earth's gravitational field overtakes the effect of the accumulator's electric field; for small charges, millicharged particles are not electrostatically bound to the shell, whereas for large charges they form bound states with electrons and cannot freely penetrate conducting surfaces.
• Figure 5: Using the results of Figs. \ref{['fig:nxCR']} and \ref{['fig:trap']}, we determine the accumulated density $n_\text{trap}$ of positively-charged millicharged particles initially produced by cosmic rays. In the top row, the notation "$E_\oplus \neq 0$" indicates that we take the millicharges to efficiently couple to the atmospheric electric field, whereas in the bottom row "$E_\oplus = 0$" indicates that the role of the atmospheric electric field is neglected (this is shown for the purpose of illustrating the enhancing effect of $E_\oplus$). For millicharged particles that couple directly to the photon, we expect that detailed modeling will result in densities similar to the results for "$E_\oplus \neq 0$." These results can be significantly modified if the interaction is mediated by a kinetically-mixed dark photon, potentially yielding densities that are parametrically larger than those shown here, depending on the specific model parameters. In gray, we also show existing limits from accelerator probes Davidson:2000hfHaas:2014ddaPrinz:1998uaArgoNeuT:2019ckqmilliQan:2021lneArguellesDelgado:2021lekPBC:2025snyCMS:2024eyxAlcott:2025rxn and SN1987A Chang:2018rso. In the left-column, "outdoors" means that the accumulator is operated $1 \ \text{m}$ above the crust, whereas in the right-column "indoors" means that the accumulator is operated inside of a room $1 \ \text{m}$ below the crust (this latter scenario is qualitatively similar to operating inside of a conducting building slightly above ground).