Residual-gas collisions and collisional heating as the limit of long-term magnetic confinement of antihydrogen: quantitative characterization of the background gas and heating rates in the trapping region

The confinement of neutral antihydrogen in cryogenic magnetic minimum-B traps for 1000 s (ALPHA, 2011) opened precision spectroscopy and antimatter-gravity experiments, but left the ultimate storage lifetime unexplained: the temperature and density of the residual background gas in the trapping region could not be quantified, giving calculated antihydrogen loss lifetimes anywhere between roughly 300 s and $10^{5}$ s and leaving collision-induced annihilation and elastic-collision heating rates undetermined. Later ALPHA work has established empirically that trapped antihydrogen survives for tens of hours (preliminary lower limits of 50-66 hours), that resonant spectroscopy confirms the atoms occupy the 1S ground state, and that production is consistent with thermal equilibrium in the positron plasma; cryogenic positron sympathetic cooling now accumulates more than 15000 atoms. What remains open is the quantitative core of the original question: a direct, in-situ determination of the residual-gas temperature and density in the trapping region, and a dedicated measurement of, or upper bound on, small collisional heating rates of trapped antihydrogen during multi-hour storage - the mechanism pair that now sets the accumulation lifetime and the systematics floor of precision measurements on antimatter.

Background

Antihydrogen ($\bar{\mathrm{H}}$), the bound state of an antiproton and a positron, is the only pure anti-atomic system accessible in the laboratory. Because the CPT theorem (invariance under combined charge conjugation, parity reversal and time reversal) requires hydrogen and antihydrogen to have identical spectra, precision spectroscopy of trapped $\bar{\mathrm{H}}$ is a sensitive test of matter-antimatter symmetry, and long storage times are what make such spectroscopy and eventual gravity measurements feasible.

Producing cold, trappable $\bar{\mathrm{H}}$ requires combining cold antiprotons and positrons. The ALPHA experiment (Antihydrogen Laser Physics Apparatus) at CERN's Antiproton Decelerator (AD) produces $\bar{\mathrm{H}}$ inside a Penning-Malmberg trap (a cylindrical charged-particle trap based on nested well electrodes in a strong solenoidal field), where antiprotons are mixed with a cryogenic positron plasma. Antihydrogen forms predominantly by three-body recombination (two positrons and one antiproton), which populates highly excited (Rydberg) states; the atoms then decay toward the ground state by radiative and collisional cascades. Neutral $\bar{\mathrm{H}}$ can be confined only if it is produced with kinetic energy below the depth of the superimposed magnetic minimum-B trap (an Ioffe-type trap made of an octupole winding plus mirror coils), which in the 2011 ALPHA apparatus was only about 0.5 K in temperature units, so only a tiny fraction of produced atoms is trappable. Antihydrogen annihilations on the trap walls are reconstructed by a silicon vertex detector, which gives both the time ($t$) and axial position ($z$) of each annihilation upon release of the trap and thereby sensitivity to the atoms' energy distribution. The trap also admits quasi-trapped orbits - atoms whose total energy exceeds the well depth but which are transiently confined while energy is shared among degrees of freedom.

In 2011 ALPHA reported confinement of $\bar{\mathrm{H}}$ for 1000 s (extending the previous 172 ms demonstration by nearly four orders of magnitude), a calculated ground-state fraction above 99% after about 0.5 s of cascade, and the first information on the kinetic energy distribution of the trapped atoms, consistent with antiprotons thermalized in the positron plasma at $T_{e^+}=54$ K (Andresen et al., Nature Physics 7, 558-564 (2011)). The paper explicitly flagged what it could not determine: the temperature and density of the background gas in the trapping region (there is a direct vacuum path to room-temperature components, so gas temperatures between 10 K and 100 K could not be excluded); whether elastic collisions with that gas heat the trapped atoms appreciably (calculated heating rates ranged over orders of magnitude, implying 0.5 K of heating anywhere between 300 s and $10^{5}$ s); the absence of a direct measurement of the internal-state distribution; the possibility that formation is epithermal and anisotropic rather than thermalized (as earlier measurements and calculations on conventional plasma merging had suggested); the fact that the detailed $t$-$z$ simulation comparison was restricted to confinement times below 1 s; and the need to increase trapping rates and reduce $T_{e^+}$.

Subsequent experimental developments define the modern context in which these questions must be judged. ALPHA-2 and ALPHA-g routinely 'stack' (accumulate) atoms over many production cycles; positron plasmas are now sympathetically cooled by laser-cooled beryllium ions; trapped samples have been laser-cooled on the 1S-2P (Lyman-\alpha, 121.6 nm) transition; the 1S-2S two-photon transition, the ground-state hyperfine spectrum (microwave transitions between the two spin configurations of the 1S state), and the effect of gravity on released antihydrogen have all been measured. These experiments all depend on, and are ultimately limited by, how long and how cold trapped $\bar{\mathrm{H}}$ can be kept, which is set by collisions with the residual gas in the cryogenic trap.

Problem Statement

The unresolved core of the 2011 confinement paper's limitation list is the quantitative characterization of the residual-gas environment and of collisional heating in long-term magnetic confinement of antihydrogen.

Several of the 2011 limitations have since been closed by direct later work and are no longer open targets: the ground state of trapped $\bar{\mathrm{H}}$ is now spectroscopically confirmed (resonant microwave hyperfine transitions, 1S-2S two-photon spectroscopy, and Lyman-\alpha laser cooling all address atoms in the 1S state); the formation question is treated as settled in favor of antiprotons thermalizing in the positron plasma (trapping yields scale as expected with positron temperature, and the trapped velocity distribution is consistent with a thermal distribution truncated at the trap depth); and the programmatic direction of raising trapping rates by lowering $T_{e^+}$ has been realized (sympathetic positron cooling, accumulation of more than 15000 simultaneously trapped atoms).

What remains open is: (1) determine the temperature and density of the residual background gas in the trapping region itself - the 2011 estimate spanned gas temperatures from 10 K to 100 K, and current values are still inferred indirectly from antiproton storage lifetimes, cryopumping behaviour, and annihilation cross-section models rather than measured in situ; (2) measure, or place a quantitative experimental upper bound on, the rate at which elastic collisions with this gas heat trapped antihydrogen during storage times of hours ($\gtrsim 10^{4}$ s), distinguishing small cumulative heating from annihilation and from the escape of quasi-trapped atoms; and (3) from these, establish the mechanism and magnitude of the observed confinement lifetime, currently reported only as estimates of roughly 50-66 hours, and assess whether heating, rather than annihilation, ultimately limits accumulation and the achievable interrogation times for precision spectroscopy and gravity measurements. A directly measured internal-state (ground-state fraction) distribution versus confinement time is the one quantity from the original list that remains unmeasured; ground-state trapping is already established spectroscopically. Items (1) and (2) are the open quantitative core, and item (3) is the interpretive consequence to be drawn from them.

References

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