Discharge Capillary Arrays for Plasma Sources

• Array of discharge capillaries are plasma-source designs constructed from repeated discharge units, operating either as literal tubes or as electromagnetic analogues like INCA.
• They enable precise control of plasma density and current channels, critical for applications such as plasma wakefield acceleration, beam focusing, and large-area processing.
• Key challenges include managing temporal density evolution, synchronizing multi-diagnostic measurements, and ensuring thermal integrity during high-repetition-rate operation.

to=arxiv_search.search 买天天中彩票 天天中彩票网站json {"query":"all:\"discharge capillaries\" OR all:\"array discharge\" OR id:(Ahr et al., 2018) OR id:(Garland et al., 2020) OR id:(Bagdasarov et al., 2017) OR id:(Crincoli et al., 24 Jul 2025)","max_results":10,"sort_by":"relevance"}result to=arxiv_search.search code 北京赛车投注 六和彩 [{"arxiv_id":"(Ahr et al., 2018)","title":"INCA - Inductively Coupled Array Discharge","authors":["T. Binder","U. Czarnetzki"],"summary":"Recently a novel concept for collisionless electron heating and plasma generation at low pressures was proposed theoretically (U Czarnetzki and Kh Tarnev, Phys. Plasmas 21 (2014) 123508). It is based on periodically structured vortex fields which produce certain electron resonances in velocity space. A more detailed investigation of the underlying theory is presented in a companion paper (U Czarnetzki, submitted to PSST (2018), (Czarnetzki, 2018). Here, the new concept is experimentally realized for the first time by the INCA (INductively Coupled Array) discharge. The periodic vortex fields are produced by an array of small planar coils. It is shown that the array can be scaled up to arbitrary dimensions while keeping its electrical characteristics. Stable operation at pressures around and below 1 Pa is demonstrated. The power coupling efficiency is characterized and an increase in the efficiency is observed with decreasing pressure. The spatial homogeneity of the discharge is investigated and the behaviour of the plasma parameters with power and pressure are presented. Linear scaling of the plasma density with power and pressure, typical for conventional inductive discharges, is observed. Most notably, the plasma potential and the corresponding mean ion energy show clear evidence for the presence of super energetic electrons, attributed to stochastic heating. In the stochastic heating mode, the electron distribution function becomes approximately Maxwellian but with increasing pressure it turns to the characteristic local distribution function known from classical inductive discharges. Large area processing or thrusters are possible applications for this new plasma source.","published":"2018-06-06","categories":["physics.plasm-ph","physics.app-ph"]},{"arxiv_id":"(Garland et al., 2020)","title":"Evolution of longitudinal plasma-density profiles in discharge capillaries for plasma wakefield accelerators","authors":["O. Delferrière","P. K. K. Maroju","M. Schuh","A. Martinez de la Ossa","M. F. Gilljohann","N. H. Matlis","V. Libov","S. Wesch","M. Gross","F. Grüner"],"summary":"Precise characterization and tailoring of the spatial and temporal evolution of plasma density within plasma sources is critical for realizing high-quality accelerated beams in plasma wakefield accelerators. The simultaneous use of two independent diagnostic techniques allowed the temporally and spatially resolved detection of plasma density with unprecedented sensitivity and enabled the characterization of the plasma temperature at local thermodynamic equilibrium in discharge capillaries. A common-path two-color laser interferometer for obtaining the average plasma density with a sensitivity of 2e15 cm^-2 was developed together with a plasma emission spectrometer for analyzing spectral line broadening profiles with a resolution of 5e15 cm^-3. Both diagnostics show good agreement when applying the spectral line broadening analysis methodology of Gigosos and Cardeñoso. Measured longitudinally resolved plasma density profiles exhibit a clear temporal evolution from an initial flat-top to a Gaussian-like shape in the first microseconds as material is ejected out from the capillary, deviating from the often-desired flat-top profile. For plasma with densities of 0.5-2.5e17 cm^-3, temperatures of 1-7 eV were indirectly measured. These measurements pave the way for highly detailed parameter tuning in plasma sources for particle accelerators and beam optics.","published":"2020-10-06","categories":["physics.acc-ph","physics.plasm-ph"]},{"arxiv_id":"(Crincoli et al., 24 Jul 2025)","title":"Advanced Ceramic Plasma Discharge Capillaries for high repetition rate operation","authors":["M. Vannini","V. Pettinacci","M. Pompili","M. Ferrario","M. Anania","P. Chiadroni"],"summary":"In view of future applications of plasma-based particle accelerators, within the fields of high-energy physics and new light sources, the capability of plasma sources to operate at high repetition rates is crucial. In particular for gas-filled plasma discharge capillaries, which allow direct control over plasma properties, a key aspect is the longevity of the material, subject to erosion due to the heat flux delivered by high voltage plasma discharges. In this regard, we present an innovative design of discharge capillaries based on the use of different ceramic materials, which can sustain high voltage plasma discharges at high repetition rate and, moreover, be easily machined for the complex geometries required for plasma-based accelerators. Experimental campaigns are carried out at 10-150 Hz, assessing the longevity of ceramic capillaries by means of different diagnostic techniques. In addition, numerical simulations are performed to analyze the heat transfer within the whole plasma source. Results from experimental and numerical analysis highlight the capability of ceramic capillaries to preserve plasma properties and the integrity of the source during long-term plasma discharge operation at high repetition rate. In particular, we demonstrated the suitability of the proposed solution for the operative range of 100-400 Hz, foreseen for EuPRAXIA@SPARC_LAB project.","published":"2025-07-24","categories":["physics.acc-ph","physics.plasm-ph"]},{"arxiv_id":"(Bagdasarov et al., 2017)","title":"On production and asymmetric focusing of flat electron beams using rectangular capillary discharge plasmas","authors":["E. N. Nerush","I. Y. Kostyukov"],"summary":"A method for the asymmetric focusing of electron bunches, based on the active plasma lensing technique is proposed. This method takes advantage of the strong inhomogeneous magnetic field generated inside the capillary discharge plasma to focus the ultrarelativistic electrons. The plasma and magnetic field parameters inside the capillary discharge are described theoretically and modeled with dissipative magnetohydrodynamic computer simulations enabling analysis of the capillaries of rectangle cross-sections. Large aspect ratio rectangular capillaries might be used to transport electron beams with high emittance asymmetries, as well as assist in forming spatially flat electron bunches for final focusing before the interaction point.","published":"2017-10-20","categories":["physics.plasm-ph","physics.acc-ph"]},{"arxiv_id":"(Czarnetzki, 2018)","title":"Stochastic electron heating in the INductively Coupled Array discharge","authors":["U. Czarnetzki"],"summary":"Recently an effective model was proposed for electron collisionless heating in a new kind of low pressure array discharge. Periodic arrays of electric field vortices create collisionless heating by resonant wave-particle interactions. Here a more detailed treatment is given of the current and power deposition under the assumption of a Maxwellian electron velocity distribution. The finite extension of the fields into the plasma is represented via an exponential decay and the resonances are collision broadened by a complex resonance function. The resonances then lead to a stochastic heating mode with non-locality and negative power deposition. The corresponding non-local conductivity is derived from first principles and compared to a limiting case based on Lieberman’s model of stochastic heating in an inductive sheath. An equivalent circuit is derived allowing for simpler models of self-consistent systems and comparison with conventional discharges. It is found that the new array discharge can have a high plasma production efficiency which exceeds the classical stochastic heating in the regime $\psi \sim 1$ as well as an inductive ohmic mode for $\psi \gg 1$, where $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$ is the ratio between the skin depth $s$ and the cell size $\Lambda$.","published":"2018-06-03","categories":["physics.plasm-ph"]}]

In the literature surveyed here, the phrase array of discharge capillaries encompasses two closely related constructions. In the literal sense, it denotes a plasma-source architecture built from repeated capillary discharge units, each acting as a confined discharge channel whose plasma density, current, and thermal state must be controlled over space and time. In a closely related electromagnetic sense, it denotes a periodically structured plasma source whose unit cells behave like capillary-like discharge microdomains without being literal tubes, as in the INductively Coupled Array (INCA), where a planar two-dimensional array of many small inductive elements generates a periodic lattice of RF vortex fields above a surface (Ahr et al., 2018). Across accelerator and low-temperature-plasma contexts, the unifying issues are unit-cell periodicity, discharge coupling, plasma-density evolution, magnetic-field topology, and survivability under repetitive loading (Garland et al., 2020, Bagdasarov et al., 2017, Crincoli et al., 24 Jul 2025).

1. Conceptual scope and terminology

The capillary-discharge literature treats a capillary as a confined plasma channel with electrodes at the ends, gas feed, and a current pulse that initiates and sustains the discharge. Such capillaries are used as plasma sources for plasma wakefield accelerators, plasma lenses, and waveguides, because they provide a confined plasma channel for wake excitation, can guide laser pulses, can focus charged beams, and, if properly tailored, can provide entrance and exit ramps that help preserve beam emittance and reduce hosing (Garland et al., 2020).

INCA generalizes the notion of repeated discharge cells in a different way. Instead of geometrical confinement in tubes, it uses a planar two-dimensional array of many small inductive elements. The resulting discharge can be viewed as an array-based plasma source, and in that sense it is closely related to the notion of an “array of discharge capillaries”: each cell of the array behaves like a small discharge unit, but unlike a set of isolated capillaries, the cells are electromagnetically coupled through the collective RF field and through the shared plasma (Ahr et al., 2018).

A central distinction therefore separates literal capillary arrays from electromagnetic analogues. In literal arrays, the locality is geometric and material. In INCA, the locality is electromagnetic and kinetic. This distinction matters because it changes the dominant coupling mechanism: wall heating, gas flow, and electrode design dominate in capillary hardware, whereas field periodicity, electron resonance, and stochastic heating dominate in the inductive analogue.

2. INCA as an electromagnetic analogue of a capillary array

INCA is presented as a fundamentally new kind of low-temperature plasma source. Rather than using one large inductive coil that generates a single azimuthal RF electric field, it uses a planar two-dimensional array of many small inductive elements, each acting like a microscopic inductive source and producing a vortex-like RF electric field in the plasma above it. When many such elements are arranged in an array, the superposition of their fields forms a periodic lattice of vortices (Ahr et al., 2018).

The physical mechanism is explicitly periodic. The array produces a periodic RF magnetic field; this induces periodically arranged azimuthal or vortex electric fields; electrons interact with the field when their transit or oscillation dynamics match the array periodicity; and the resulting heating can be stochastic, meaning that energy gain becomes chaotic due to repeated phase slippage between electron motion and the time-varying structured field. A companion theoretical treatment analyzes the underlying electron-heating model in greater detail (Czarnetzki, 2018).

Experimentally, INCA is realized as a two-dimensional planar array of small coils located below a dielectric or discharge window. Each coil is fed so that the overall structure acts as a single RF-powered source, but the local field is spatially periodic. Stable operation at pressures around and below $1$ Pa is demonstrated, and the discharge is especially suited to a low-pressure, capacitively weak, inductive regime in which energetic electrons are produced by the periodic array fields rather than by sheath-dominated acceleration (Ahr et al., 2018).

Several experimentally reported features give the capillary-array analogy its technical substance. The array can be scaled up to arbitrary dimensions while keeping its electrical characteristics. Power coupling efficiency increases with decreasing pressure. Plasma density scales linearly with power and pressure, typical for conventional inductive discharges. Most notably, the plasma potential and the corresponding mean ion energy show clear evidence for the presence of super energetic electrons, attributed to stochastic heating. In the stochastic heating mode, the electron distribution function becomes approximately Maxwellian, but with increasing pressure it turns to the characteristic local distribution function known from classical inductive discharges (Ahr et al., 2018).

A common misconception is to treat INCA as a set of literal capillaries. The literature explicitly rejects that interpretation. These are not physical capillaries; the confinement is electromagnetic and kinetic, not geometrical. The capillary analogy is useful only to the extent that each unit cell acts like a localized discharge microdomain within a collectively sustained plasma.

3. Discharge capillaries as dynamic plasma sources

For accelerator applications, discharge capillaries are not static pipes filled with uniform plasma. A sapphire discharge capillary with a central cylindrical channel, open ends, and electrodes at both ends was studied with lengths of $20$ mm and $33$ mm and diameters of $1.0$ mm or $1.5$ mm. Gas was fed into a buffer volume and then into the capillary, where a $\psi \gg 1$0 A, approximately flat-top $\psi \gg 1$1 ns current pulse from a pulse forming network initiated and sustained the discharge. The cell operated in vacuum at $\psi \gg 1$2 mbar, and the main gas mixture was $\psi \gg 1$3 argon / $\psi \gg 1$4 hydrogen (Garland et al., 2020).

In plasma wakefield accelerators, the local plasma density sets the wakefield strength, beam focusing, and the matching conditions seen by the drive and witness beams. The cited scaling is

$\psi \gg 1$5

so the actual longitudinal density distribution inside the capillary is an accelerator-relevant quantity rather than a secondary diagnostic detail (Garland et al., 2020).

The key physical result is temporal evolution of the longitudinal plasma-density profile. During the current pulse, the plasma density rises quickly and the central region exhibits an approximately flat-top longitudinal profile. After the pulse ends, the profile changes: plasma is expelled from the capillary ends into the gas inlet regions, the central flat-top region shrinks, and after about $\psi \gg 1$6s the profile becomes noticeably Gaussian-like. Measured plasma densities lie in the range $\psi \gg 1$7, while inferred temperatures lie in the range $\psi \gg 1$8, with no temperature above $\psi \gg 1$9 observed (Garland et al., 2020).

This temporal evolution has direct implications for any future array implementation. A literal array of capillaries would inherit the same issue channel by channel: the desired flat-top state exists only during a limited temporal window, and the relation between beam arrival time, discharge timing, and plasma profile is therefore intrinsic to performance. The source must be treated as a dynamic plasma source, not as a static uniform medium.

4. Diagnostics for density, temperature, and profile control

Two complementary diagnostics were used to characterize discharge capillaries with high spatial and temporal sensitivity. The first was a common-path two-color laser interferometer using an $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$0 nm Ti:sapphire laser and a BBO-generated second harmonic at $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$1 nm. The phase shift was used to infer the on-axis average electron density through

$\psi = s k_0 = \frac{2 \pi s}{\Lambda}$2

with group-velocity effects negligible up to densities of about $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$3. The interferometer sensitivity was $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$4, the temporal resolution was about $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$5 ns, and the density resolution was about $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$6 (Garland et al., 2020).

The second diagnostic was a plasma emission spectrometer analyzing the $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$7 line at $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$8 nm with Stark broadening. The relevant specifications were $\psi = s k_0 = \frac{2 \pi s}{\Lambda}$9 nm/pixel spectral resolution, intrinsic setup broadening of $s$0 nm, spatial resolution of about $s$1m, temporal resolution of about $s$2 ns, and a broadening-based density detection limit around $s$3. Hydrogen was used as a tracer species, added at $s$4 in the argon mixture, because the $s$5 Stark width is a strong density diagnostic in the relevant density range (Garland et al., 2020).

The fitting workflow was also explicit. Background was subtracted using a no-plasma spectrum, continuum emission was removed by fitting a Planck function, visible peaks were fitted using the Faddeeva function, the Gaussian component was fixed at the instrument width, and the Lorentzian width of the $s$6 line was extracted and used to infer density. Self-absorption was negligible because of the relatively low density and the small line-of-sight distance of $s$7 mm. To connect Stark broadening with temperature and density, the analysis used the tabulated or computed Stark profiles of Gigosos and Cardeñoso, interpolated in log-space. The experimental input was the longitudinal average Stark width

$s$8

The significance of the diagnostic agreement is methodological. The interferometer provides density calibration, while the spectrometer provides longitudinally resolved structure. Their agreement validates the use of spectroscopic broadening to obtain absolute density profiles instead of relying on rough temperature estimates. A plausible implication for an array of discharge capillaries is that comparable multi-diagnostic schemes would be required to establish channel-to-channel reproducibility and temporal synchronization, although those array-specific measurements are not reported here.

5. Geometry-dependent current channels and anisotropic focusing

Capillary discharge plasmas also function as current-driven magnetic optics. A rectangular capillary filled with hydrogen gas and driven by an externally supplied current pulse was proposed as an active plasma lens for asymmetric focusing of ultrarelativistic electron bunches. The simulated geometry had a $s$9 aspect ratio with

$\Lambda$0

and homogeneous initial hydrogen density

$\Lambda$1

corresponding to

$\Lambda$2

if fully ionized. The external current profile peaked at $\Lambda$3 A at $\Lambda$4 ns, and the discharge was initialized with $\Lambda$5 (Bagdasarov et al., 2017).

The active-plasma-lensing principle relies on the azimuthal magnetic field generated by the discharge current. In a circular capillary, the field is azimuthally symmetric and focuses in both transverse directions. In a rectangular capillary, symmetry is broken. For a large aspect ratio, the magnetic field near the center becomes approximately one-dimensional, so the gradient across the short dimension is much stronger than across the long dimension. That produces different focal lengths in $\Lambda$6 and $\Lambda$7, i.e. asymmetric focusing (Bagdasarov et al., 2017).

The simulations show that after an initial ionization and heating stage of about $\Lambda$8 ns, the plasma reaches a quasi-steady state, while the long dimension equilibrates more slowly and reaches a near-steady state in $\Lambda$9 after about $1$0 ns. At $1$1 ns, the reported center density is

$1$2

with magnetic gradients

$1$3

whose ratio is approximately $1$4, of the order of the capillary aspect ratio (Bagdasarov et al., 2017).

Near-axis fitted profiles are

$1$5

and

$1$6

These relations show an even density profile and an approximately linear magnetic field near the axis with cubic corrections. The paper concludes that large-aspect-ratio rectangular capillaries can serve as compact active plasma lenses for asymmetric beam transport, beam shaping, and formation of spatially flat bunches before final focus (Bagdasarov et al., 2017).

For the broader topic of arrays, the importance of this result is that unit-cell geometry is not a secondary mechanical detail. It sets the field gradients, and therefore the optical function, of each discharge channel. An array assembled from such units would inherit geometry-dependent anisotropy at the cell level.

6. Materials, thermal management, and high-repetition-rate operation

High-repetition-rate operation shifts the design problem from single-shot plasma formation to cumulative thermal loading and material survivability. An advanced ceramic capillary design was developed for future plasma-based particle accelerators and light-source facilities, motivated in particular by the $1$7 Hz operational range foreseen for EuPRAXIA@SPARC_LAB. The experimental source consisted of a Shapal Hi M Soft capillary inserted into a Macor holder with metal electrodes at the ends (Crincoli et al., 24 Jul 2025).

The main geometric details were a capillary length of $1$8 cm, a channel diameter of $1$9 mm, and two gas inlets each of $20$0 mm diameter. The capillary material, Shapal Hi M Soft, was described as a machinable Aluminum Nitride ceramic mixed with Boron Nitride, with thermal conductivity of $20$1 at room temperature and $20$2 at $20$3C, and a melting temperature of $20$4C in vacuum. The holder material, Macor, had thermal conductivity of $20$5 at room temperature and maximum operating temperature of $20$6C. The electrodes combined an inner molybdenum ring and an outer stainless-steel plate; molybdenum was chosen because of its very high melting temperature of $20$7C (Crincoli et al., 24 Jul 2025).

The high-repetition-rate tests used a continuous-flow gas mixture of $20$8 ($20$9) + $33$0 ($33$1), chamber pressure around $33$2 mbar, and capillary gas pressure $33$3 mbar. The discharge repetition rate was scanned over $33$4 Hz. The paper repeatedly emphasizes suitability for the $33$5 Hz range and reports that the upper experimental limit of $33$6 Hz was set by the maximum current capability of the HV generator rather than by a fundamental source limit (Crincoli et al., 24 Jul 2025).

Electrical and thermal characterization were cast in terms of Joule heating and heat conduction: $33$7 Electron temperature was estimated using the quasi-static Bobrova model,

$33$8

The whole-source thermal simulation in COMSOL Multiphysics 6.1 included the Shapal capillary, Macor holder, HV cables, and gas injection pipe; the HV cables and vacuum chamber acted as heat sinks, while external surfaces were thermally insulated to represent vacuum conditions (Crincoli et al., 24 Jul 2025).

The quantitative endurance result was $33$9 million discharges at $1.0$0 Hz with no modification observed in the whole source, plasma properties maintained, and capillary integrity preserved. Spectroscopy showed electron density around $1.0$1 at peak, a hollow transverse density profile during formation, a Gaussian-like profile during recombination, and stable profiles over repeated operation. Thermal simulations predicted steady state after about $1.0$2 hours and a maximum capillary temperature of about $1.0$3C at $1.0$4 Hz; at $1.0$5 Hz, equilibrium temperature stayed below the melting temperatures of Macor and Shapal. Beyond the modeled safe operating range, Macor’s melting temperature became the limiting factor, and the proposed route to higher repetition rate was reducing pulse energy by lowering current and or pulse duration (Crincoli et al., 24 Jul 2025).

7. Applications, misconceptions, and unresolved scaling questions

The application space spans low-temperature plasma processing, propulsion, and advanced accelerators. INCA is proposed for large-area processing and thrusters because the array can be scaled almost arbitrarily in lateral dimensions while keeping the unit-cell geometry and driving conditions similar (Ahr et al., 2018). Capillary discharges are used for plasma wakefield acceleration, beam optics, active plasma lenses, and waveguides, and rectangular capillaries are specifically proposed for transport of beams with emittance asymmetry and for formation of flat electron or ion bunches before final focusing (Garland et al., 2020, Bagdasarov et al., 2017).

Several misconceptions are directly corrected by the cited work. First, an array-like plasma source need not be an array of literal tubes: INCA is an electromagnetic analogue, not a set of physical capillaries (Ahr et al., 2018). Second, a discharge capillary does not necessarily preserve the flat density profile often assumed in accelerator design; the longitudinal profile evolves in time from an initial flat-top to a Gaussian-like shape in the first microseconds (Garland et al., 2020). Third, high-repetition-rate survivability cannot be inferred from single-shot operation, because the main scaling constraint is cumulative heat removal rather than ignition alone (Crincoli et al., 24 Jul 2025).

The unresolved issues are also explicit. The ceramic-capillary study strongly supports the feasibility of a high-repetition-rate discharge-capillary platform as a materials-and-thermal-engineering concept, and it identifies thermal management as the key scaling constraint. However, it does not directly address cross-talk between neighboring capillaries, shared gas distribution in an array, synchronization of multiple discharges, distributed pumping, or array-level electromagnetic interference. A plausible implication is that these effects, rather than single-capillary plasma formation, become the decisive systems problem when moving from one capillary to an actual array (Crincoli et al., 24 Jul 2025).

Taken together, the literature defines an array of discharge capillaries not as a single standardized device but as a design space organized around repeated plasma-generating unit cells. In one branch, the units are literal capillary discharges whose density profiles, magnetic gradients, and thermal cycling determine accelerator performance. In the other, represented by INCA, the units are periodically arranged inductive vortices that realize capillary-like locality through field structure rather than walls. The common technical theme is controlled periodicity: periodicity in geometry, in current channels, in RF field structure, and in thermal loading.