Influence of released surface electrons on the pre-ionization of helium barrier discharges: laser photodesorption experiment and 1D fluid simulation

The presented work highlights the role of residual weakly-bound surface electrons acting as an effective seed electron reservoir that favors the pre-ionization of diffuse barrier discharges (BDs). A glow-like BD was operated in helium at a pressure of 500 mbar in between two plane electrodes each covered with float glass at a distance of 3 mm . The change in discharge development due to laser photodesorption of surface electrons was studied by electrical measurements and optical emission spectroscopy. Moreover, a 1D numerical fluid model of the diffuse discharge allowed the simulation of the laser photodesorption experiment, the estimation of the released surface electrons, and the understanding of their impact on the reaction kinetics in the volume. The breakdown voltage is clearly reduced when the laser beam at photon energy of 2.33 eV hits the cathodic dielectric that is charged with residual electrons during the discharge pre-phase. According to the adapted simulation, the laser releases only a small amount of surface electrons in the order of 10 pC . Nevertheless, this significantly supports the pre-ionization. Using a lower photon energy of 1.17 eV , the transition from the glow mode to the Townsend mode is induced due to a much higher electron yield up to 1 nC . In this case, both experiment and simulation indicate a retarded stepwise release of surface electrons initiated by the low laser photon energy.


Introduction
Barrier discharges (BDs) belong to the most common discharge types for industrial applications at atmospheric pressure [1][2][3]. Dielectric-covered electrodes restrict the breakdown current which allows the generation of nonequilibrium plasmas. Moreover, BDs are quite promising due to high chemical reactivity at comparatively low power consumption. That is why this discharge type has become indispensable for the surface treatment and modification of heat-sensitive materials as well as for biomedical use [4,5]. In this context, the key position is addressed to laterally diffuse BDs, often referred to as the atmospheric-pressure glow discharge and the atmospheric-pressure Townsend discharge, respectively [6].
A crucial formation criterion for diffuse BDs is assigned to a sufficient pre-ionization, e.g., by secondary electron emission (SEE) and Penning ionization requiring the presence of species in metastable states. In this way, the long-living species act as a memory between consecutive discharge breakdowns. Also, the effective ionization rate during the breakdown must be moderate to avoid critical space charge formation and streamer development, and to allow an overlap of wide electron avalanches in lateral direction. For these reasons, diffuse BDs are typically operated in helium and nitrogen [7][8][9][10][11]. However, diffuse BDs are also observed in oxygen-containing systems, especially, when the operating frequency is low [7,12,13]. Since oxygen quenches the metastable states, their effective lifetime becomes much shorter than the discharge off-time under these conditions. As a consequence, another source of seed electrons must exist that provides the required pre-ionization. One possible and recently discussed process is the thermal desorption of residual weakly-bound electrons from the dielectric surface [14].
The accumulation of charge carriers at dielectric surfaces is most characteristic of BDs. Up to now, the physical nature of surface charges, their trapping and binding mechanisms, and their interaction with the discharge species are controversially discussed. It is assumed that negative surface charges are adsorbed electrons with low material-dependent binding energy. These electrons are either trapped in the shallow image potential just in front of the crystallographic boundary or in the conduction band (CB) just inside the dielectric, which depends on the solid's electron affinity [15,16]. However, in general consensus, positive surface charges are defect electrons (positive holes) in the valance band caused by recombination of positive ions with electrons at the dielectric surface [17,18].
Indeed, investigations of thermally stimulated current, thermoluminescence and optically stimulated luminescence revealed electron trapping centers in the order of 1 eV, which differs significantly from the valence-band electrons [19,20]. Consequently, surface electrons can be removed more easily than intrinsic electrons, wherefore one has to distinguish between both species. The release of residual surface electrons by thermal influence, photons, excited species or radicals is assumed to favor the pre-ionization of diffuse BDs [17,21,22]. Experiments revealed that the lower the binding energy of surface electrons depending on the dielectric material, the higher is the probability to operate diffuse BDs in air [19]. Besides, streamer breakdown in air can be selfsynchronized and triggered via surface electron desorption by incident photons coming from the discharge [23], and laser photons [24], respectively.
The presented work investigates the effect of released surface electrons on the pre-ionization of the diffuse BD in helium. Besides the laser photodesorption experiment, a onedimensional numerical fluid simulation provides information about the influence of released surface electrons on the reaction kinetics in the discharge volume. The outline of this article is as follows. The experimental setup and the diagnostics are described in section 2. Section 3 briefly points out the most important features of the modeling. Finally, the characteristics of the laser photodesorption effect and its influence on the discharge mode are discussed in section 4 and section 5, respectively.

Experimental setup and methodology
2.1. Discharge configuration and gas supply Figure 1 shows the plane-parallel discharge configuration. The high-voltage driven electrode made of copper as well as the grounded aluminum block were covered with float glass (thickness of 0.7 mm, permittivity of 7.6). Gap spacers (not drawn in the figure) made of polyether ether ketone defined the discharge gap width of 3 mm. Four sidewise oriented orifices enabled the direct gas supply, the investigation of the optical emission from the discharge volume, and the laser guidance. The discharge cell was placed inside a vacuum chamber made of stainless steel that was pumped to a base pressure below -10 mbar 5 before it was filled with helium (purity > 99.999%). The operating pressure of 500 mbar was kept constant in the flowing regime (100 sccm) using a process pump (TRIVAC D25BCSPFPE) in combination with a diaphragm pressure gauge and a butterfly valve (MKS).

Electrical measurements
The discharge was operated with a sine-wave voltage ( ) U t ext at a frequency of 2 kHz provided by a power supply (Trek PM04015). As illustrated in figure 2, the total transported  at the grounded electrode. The electrical signals were recorded by a digital oscilloscope (LeCroy 9304AM). The gap voltage the discharge current without any displacement current were recalculated by means of an appropriate electrical equivalent circuit, introduced in [25,26]. Here, C gap and C die are the capacitances of the gas gap and the dielectrics, respectively. Both quantities are calculated based on the assumption that the lateral discharge extent equals the circular electrode area = A 1.1 cm 2 . C tot is the total cell capacitance derived from the flat slope of the ( ) Q U ext ext plot (Lissajous figure), and = - die is the parallel capacitance beyond the lateral discharge extent.

Optical emission spectroscopy
The optical emission originating from the discharge volume was depicted by a vertically moveable lens and detected by a photomultiplier tube (PMT, Hamamatsu R928) in combination with a monochromator (MC, Acton Research Corporation, SpectraPro, focal length of 500 mm). The width of the horizontal slit at the entrance of the MC was 0.2 mm, and the lens was moved in steps of 0.1 mm. The spectral resolution of 1 nm results from the fixed -1200 mm 1 grating and the adjustable width of the vertical slits just in front and behind the MC. The PMT signal was recorded by the digital oscilloscope with a temporal resolution of m 0.1 s.

Laser photodesorption
The photodesorption experiment was performed by means of a Nd:YAG laser (Quanta Ray GCR 130, 10 Hz repetition rate, 170 mJ maximum energy, 10 ns pulse duration). As the second harmonic wavelength l = 532 nm lsr was used, then the fundamental wavelength l = 1064 nm lsr was filtered out by a beam dump and vice versa (see figure 2). A system of mirrors that were highly reflective for both laser wavelengths enabled the vertical beam alignment. Thereafter, a cylindrical lens (focal length of -300 mm) focused the laser beam only vertically in order to pass the discharge gap width of 3 mm just behind the focus. In the center of the discharge volume, the elliptical cross-sectional area of the laser beam was defined by the vertical half-axis of about 0.5 mm and the horizontal half-axis of about 4.5 mm. Finally, the slight divergence of the laser beam enabled the photodesorption of surface electrons at a small angle of incidence.
Moreover, the laser pulse energy (E lsr ) was detected by a power meter (COHERENT, FieldMaxII) located behind the vacuum chamber. The maximum pulse energy inside the discharge volume was about = ( ) E 532 nm 70 mJ lsr and = ( ) E 1064 nm 110 mJ lsr , respectively. Furthermore, the laser pulse was shifted along the phase of the feeding voltage by means of a pulse delay generator (SMV PDG 204). The experiment was triggered by the laser pulse train at 10 Hz. Each time, up to four consecutive discharge cycles at the operating frequency of 2 kHz were recorded in order to analyze the laser-induced change in discharge characteristics and its relaxation behavior.

Simulation of the discharge
A detailed description of the one-dimensional fluid simulation regarding the balance equations, boundary conditions, numerics, and parameter variations is given in [22]. However, this time, the simulation considered small (synthetic) air impurities, defined by the density ratio , instead of small admixtures of oxygen to helium. A minimum set of relevant species and reactions, summarized in table 1, was used which enabled the simulation to represent the main discharge characteristics from the experiment.
The ground-state neutral species He, N 2 , and O 2 act as the background gas, and the charged species are electrons and the positive ions He + , He 2 + , + N 2 , + N 4 , + O 2 , and + O 4 . Negative ion formation was ignored in the present simulation since the concentration of oxygen impurities is only around 20 ppm, and the previous simulation of the discharge in helium with 400 ppm oxygen admixture revealed no remarkable influence of negative ions and related processes on the discharge development [22]. Metastable atoms He m and dimers He 2 m are included as well as further resonantly excited He states serving as immediate sources of UV and VIS photons. Note that the VIS radiation relaxation is only simulated for comparison with the measured optical emission from the experiment. The rate coefficients for excitation and ionization by electron impact were calculated using BOLSIG+ and the cross sections taken from lxcat.net and the Lisbon database [27, 29, 30], and for heavy particle collisions from [5,28,31]. Note that the stated rate coefficient for recombination of + O 2 ions with electrons is the sum over several dissociative and non-dissociative reaction channels, given in [31]. Electrons reaching the dielectric surface are fully absorbed, ions become neutralized, and He metastable states become deexcited. Here, SEE is considered for incident ions (g + ), metastable states (g m ), and UV photons (g ph ). Moreover, thermal desorption of surface electrons is included in the simulation, as proposed in [17].
The electron transport parameters were obtained as a function of the reduced electric field strength E/n using BOLSIG+. As motivated in [17], the axial electric field distribution e e = ( ) , 0 r was calculated analytically from the electric displacement field ( ) D z t , , which allows a fast determination of the electric field in 1D compared to the numerical solution of the Poisson's equation. Therefore, Gauss's law was integrated stepwise for the dielectrics and the gas gap. Here, r ( ) z t , is the charge density distribution inside the gas gap, and s ( ) t 1 and s ( ) t 2 are the surface charge densities on both dielectrics. Two boundary conditions must be considered. Firstly, the total charge is conserved, Secondly, the unspecified integration constant resulting from the stepwise integration of Gauss's law (4) was determined by the equivalence of the axially integrated electric field and the applied voltage Here, d and g are the widths of the dielectrics and the gas gap, respectively. Finally, the analytical formula for the spatiotemporal electric field distribution inside the gas gap ) reads e e s e e = -+ Moreover, the balance equation for the density n k of species k at position z and time t, k k k was solved numerically using the Euler method in combination with different dynamic time steps for fast and slow collision processes, allowing a maximum change in the species densities of 5% from one to another time step. This limit is a compromise between the computing time, the calculation accuracy and the stability of the simulation. However, using 2% or 10% does not result in significant changes in the discharge characteristics. In equation (9), ( ) S z t , k is the total rate of production and loss by collisions, and G ( ) z t , k denotes the total flux of the species density ( ) n z t , k , including the diffusion flux for neutral particles , 10 diff k k k and, additionally, the drift flux for charged particles is the mobility of the charged particles. Regarding the numerical discretization, a centered scheme was used for the diffusion flux, whereas the drift flux was handled by an upwind scheme. More details regarding the numerics can be found in [22].

Adaption to the experiment
The next step was the adaption of the simulation to the experiment, since the actual effect caused by laser photodesorption of surface electrons is very sensitive to the initial discharge characteristics. Therefore, the density of air impurities = + n n n air N O 2 2 , the gas temperature T g , the SEE coefficients g + and g ph , and the electron flux J e des caused by thermal desorption were varied. Their respective influence on the discharge was separately discussed in [22]. Several parameter sets result in a satisfying agreement with the discharge characteristics from the experiment, and reproduce the laser photodesorption effect as well. However, for the further discussion we chose one parameter set. Figure 3 presents the discharge characteristics from experiment compared to the adapted simulation. 3 ) emission at l = 706.5 nm, the simulated excitation rate of the radiative He(3 S 3 ) state, and the reduced electric field strength are depicted. The discharge current pulse, the gap voltage drop, the cathode-directed ionization front, and the absence of a positive column are well-reproduced by the simulation. Note that the simulated gap voltage drop lasts longer. Probably, the electron-ion recombination during the afterglow might be too slow to describe the experiment with consideration of the used set of reactions in table 1, as also pointed out in [32]. But, the investigated laser photodesorption effect influences primarily the well-reproduced discharge pre-phase and the breakdown. Moreover, in (e) and (f), the spatially averaged particle-density profiles and the contribution of ions, helium metastable states, UV photons, and thermal desorption to the total SEE flux are plotted, respectively. During the early discharge pre-phase, the thermal desorption of surface electrons from the cathodic dielectric clearly dominates and provides the required pre-ionization. But, during the late prephase as well as during the breakdown, the SEE by ions and UV photons determines the total SEE flux.
Note that the simulation does not account for radiation trapping, which means that the excitation of the He( P 2 1 ) state results in UV photons by radiation relaxation to the ground state, but it does not consider de-excitation to metastable states. As a consequence, the simulation might over-predict the SEE by UV photons. However, since the SEE by ions is in the same order of magnitude, the effect of missing radiation trapping remains small. This can be compensated by a reasonable increase of the SEE coefficient for ions from 0.2 to 0.25 when the excitation of He( P 2 1 ) ends in the metastable state, only. In a current work under identical discharge conditions [33], it was estimated by Townsend's criterion for the breakdown voltage that effective SEE coefficients may lie between 0.04 and 0.4 depending on the (charged) dielectric material. Also, the rates for electron-impact excitation of He( S 2 1 ) and He( S 2 3 ) are clearly larger than for He( P 2 1 ) at low electric fields, wherefore the metastable densities are not remarkably influenced by radiation trapping.

Simulation of laser photodesorption
Modeling the complex interaction between the laser photons and the charged dielectric surface is beyond the scope of this work, since the number density of incoming laser photons is not well-defined, and the photodesorption probabilities as well as the binding energy of electrons adsorbed to an impure dielectric are not well-known. Instead, laser photodesorption of surface electrons was implemented in the simulation by removing a defined surface electron density se tot . During the laser pulse duration of = T 10 ns lsr at the firing time t lsr , that is varied with respect to the phase of the feeding voltage, the time-dependence of the released surface electron density is calculated by a Gaussian distribution, Actually, the temporal shape of the laser pulse is not crucial since the pulse duration T lsr is short compared to the ms time scale of the discharge development. But, this is the most realistic shape and its smoothness stabilizes the numerics. The released surface electrons are put into the first grid cell next to the dielectric and, then, they can either diffuse back and become adsorbed again or they drift towards the discharge volume and multiply by ionization processes. Note that this boundary condition is the same as for secondary electrons and electrons from the discharge volume [34]. Finally, se tot was varied to adapt the simulated effect to the laser photodesorption effect from experiment. In this way, se tot may represent the charge density of surface electrons released by the laser.

Effect on electrical discharge characteristics
Starting with the experimental results, figure 4 shows the change in electrical discharge characteristics caused by laser photodesorption of surface electrons. Here, the sine-wave feeding voltage , and the surface charge density s ( ) t sur on the laser-exposed dielectric are plotted for three consecutive discharge cycles, both with laser pulse (colored lines) and, for reference, without laser pulse (gray lines). The laser beam hits the negatively charged cathodic dielectric during the discharge pre-phase. The laser wavelength l = 532 nm lsr is used at the maximum pulse energy = E 70 mJ lsr . According to the literature [19,24], the corresponding photon energy = E 2.33 eV ph is high enough to release weakly-bound surface electrons from the glass-coated electrodes.
At first, no additional laser-induced current pulse or corresponding change in surface charge density s ( ) t sur is observed. Hence, it follows that the amount of electrons -Q e tot released by laser photons is below the detection limit, which allows at least the rough estimation of an upper limit for -Q e tot : taking into account the measuring capacitance of 3.4 nF, typical signal amplitudes of a few volts, and the 12 bit vertical resolution of the oscilloscope, the resolution limit is in the order of tens of pC. Although no immediate effect occurs coinciding with the laser pulse, the laser-influenced discharge ignites at a clearly lower gap voltage (DU ) and thus earlier (Dt) than the discharge without laser pulse. That means the released electrons significantly support the pre-ionization. Moreover, the lower breakdown voltage causes a smaller amount of transported charge and deposited charge density ( s D ). Because of the surface charge memory effect, the discharge breakdown during the following half-cycle starts later. Thereafter, the laser-affected discharge characteristics reconstitute within the two following voltage periods, since the discharge development is controlled by the unchanged operating conditions such as the feeding gas and the applied voltage. Hence, the influence of long-term effects due to laser-heating of the dielectric surface can be excluded.
Increasing the feeding voltage amplitude from = U 0.8 kV ext to = U 1.15 kV ext causes two discharge breakdowns per half-cycle. Under these conditions, the laser photodesorption effect is shown in figure 5. Both the electrical measurements and the spatio-temporal evolution of the optical emission revealed that the first discharge breakdown operates in the glow mode and the second one in the Townsend mode. The first glow-like discharge breakdown is directly influenced by laser photodesorption of surface electrons during its pre-phase at m = t 225 s lsr . The characteristic changes in the electrical discharge quantities are the same as already discussed for one breakdown per half-cycle in figure 4. However, this time the discharge is not disturbed for some voltage periods. Instead, the initial discharge characteristics are reconstituted already after the second breakdown within the same half-cycle. Due to the less deposited surface charge after the first laser-affected breakdown, the ignition voltage for the second breakdown is reached earlier in comparison to the discharge behavior without laser pulse. Once the ignition voltage for the second discharge breakdown has been reached it keeps constant as long as the sine-wave feeding voltage is rising. This is typical for the Townsend discharge mechanism which explains the full compensation of the laser-induced disturbance.

Influence on reaction kinetics in the volume
In figure 6, the simulated discharge characteristics are plotted without laser (gray lines) and with artificial release of s = --12 pC cm e tot 2 surface electron density (colored lines), which matches the best with the laser photodesorption effect from experiment in figure 4. Above, the gap voltage ( ) U t gap and the discharge current ( ) I t dis are plotted. In good agreement with the experiment, the simulation reveals a lower ignition voltage, corresponding earlier breakdown onset, and less transported charge when additional electrons are released from the cathodic dielectric during the pre-phase. Below, the dynamics of the spatially averaged densities of electrons, positive ions (in total), and He metastable states are shown. Even this comparatively small amount of additionally released surface electrons significantly supports the preionization, because the initial volume electron density is very low during the early pre-phase. At first, the volume electron density rises immediately by two orders of magnitude due to laser photodesorption of surface electrons   Thereby, the increase in the densities of + N 2 and + O 2 is delayed, and the volume electron density keeps high after the first short-lived laser-induced peak. Finally, the additional positive ions move to the cathodic dielectric and enhance the yield of secondary electrons The disturbance in the species densities with respect to the ordinary development without laser interaction (gray lines) lasts for some tens of microseconds, which is mainly due to the effective lifetime of the metastable states. Summarized, the laser-enhanced pre-ionization does not reconstitute until the breakdown onset, wherefore the discharge characteristics finally change. Inversely, especially because of the lower gap voltage during the discharge current pulse, the densities of electrons, He metastable states and ions are slightly reduced during the laser-affected discharge breakdown in comparison to the unaffected discharge. As a result, the overall amount of transported charge is less for the laser-disturbed discharge. The favoring of pre-ionization due to the presence of few additional electrons was also discussed in studies concerning the laser-induced branching and guiding of streamers in air [35,36], and laser photodetachment of negative ions in diffuse helium-oxygen BDs [37]. These investigations and the present work have in common that no laser-induced current is detected due to the marginal number of additional electrons. But, these electrons are sufficient to enhance the ionization rate which, later on, results in notable effects on the discharge breakdown. From this point of view, these results underline the significance of a small amount of seed electrons for the required pre-ionization to form diffuse BDs. Especially, for the standard operation of diffuse BDs driven by low operating frequency, these seed electrons might be provided by thermal desorption of surface electrons, as assumed in [14,17,22].

Parameter variations
In figure 7, the laser photodesorption effect, quantified by the earlier ignition onset Dt and the difference in surface charge density s D , is depicted in dependence of the axial laser beam position. The laser is fired during the discharge pre-phase with maximum pulse energy = ( ) E 532 nm 70 mJ lsr resulting in the largest effect on the discharge. The discharge characteristics change only if the laser beam hits the cathodic dielectric that is charged with residual surface electrons. There is no effect at all if the laser beam passes the gas gap or hits the positively charged anodic dielectric. Thus, the laser photon energy is insufficient to create additional charge carriers in the volume. As well, there is no significant contribution of laser photodetachment of negative ions to the observed effect on the discharge, since the oxygen concentration in the order of 20 ppm is too low in the present experiment. Note that a measurable effect by laser photdetachment of negative ions in the volume was reported for at least 400 ppm oxygen admixture to helium under otherwise similar discharge conditions [37]. When the laser hits the anodic dielectric, no weakly-bound surface electrons are present, and the photon energy is too low to release electrons from the valence band. However, even if electrons would be removed from the anodic dielectric, they will be retarded by the electric field. Since the vertical extent of the laser beam is approximately 1mm inside the discharge gap, the effect occurs already for a distance of about 0.5 mm to the cathodic  dielectric. As the laser beam comes closer to the cathodic dielectric, Dt and s D increase monotonously but not linearly. The reason is that the axial distribution of the laser radiation intensity differs from a homogenous profile. Therefore, the variation of the axial laser beam position changes both the effective illumination area as well as the density of incoming laser photons.
Since Dt and s D are correlated and both quantify the same laser-induced effect, only Dt is considered in the following discussion. Figure 8 depicts the laser photodesorption effect when shifting the laser pulse in time steps of m 5 s over a full discharge cycle. The periodic changes in surface charge polarity and electric field direction across the gas gap are illustrated in (a). Below in (b), the feeding voltage ( ) U t ext , the gap voltage ( ) U t gap , and the discharge current ( ) I t dis are plotted for the discharge without laser interaction. The highlighted times t 1 to t 4 mark the zero-crossings of the gap voltage and the breakdown onsets, respectively. In (c), the laser-induced time shift Dt of the breakdown onset is shown in dependence of the moment of the laser pulse. The laser photodesorption effect is significant only if the laser pulse was set between t 1 and t 2 , which marks the pre-phase of the discharge in the negative half-cycle. It starts with the zerocrossing of the gap voltage and it ends just after the onset of the discharge breakdown. Hence, the laser photodesorption effect occurs only when the laser hits the cathodic dielectric charged with residual surface electrons. In this case, the released electrons are able to pass the discharge gap on their way to the anode and, thereby, they enhance the pre-ionization. Although the upper dielectric is already charged with surface electrons before t 1 , at this time the gap voltage polarity prohibits the movement of the laser-released electrons through the gas gap. Nonetheless, one should note that a very small effect is observed before t 1 too, indicating low ionization by the released electrons in front of the upper dielectric. Vice versa, during the pre-phase of the positive halfcycle between t 3 and t 4 , the gap voltage polarity would allow a laser-induced effect, but no surface electrons are bound to the anodic dielectric at this time.
In figure 9, the laser photodesorption effect, quantified by the time shift Dt of the breakdown onset, is shown in dependence of the laser pulse energy E lsr (experiment) and the released surface electron density se tot (simulation). In (a) and (b), Dt is plotted as a function of the moment of the laser pulse during the discharge pre-phase for different values of E lsr and se tot , respectively. In (c), the quantity Dt, that is averaged over the respective temporal profile in (a), is plotted  as a function of E lsr . In (d), the simulated quantity Dt for the laser pulse at m = t 250 s lsr is plotted as a function of se tot in double-logarithmic scale. The higher the laser pulse energy, the higher is the density of incoming photons and the larger is the amount of released electrons. Therefore, the laser photodesorption effect rises both with increasing E lsr and se tot . The profiles in (a) agree qualitatively and quantitatively well with those in (b). However, the maximum in Dt occurs at different laser pulse times comparing experiment and simulation. Moreover, in (c) the slope of D ( ) t E lsr increases with increasing E lsr , whereas in (d) the slope of s D -( ) t e tot decreases with increasing se tot . Most likely this discrepancy is associated with a change in the cross-sectional area and the axial intensity distribution of the laser beam by variation of E lsr . It should be mentioned as well, that not all of the initially released electrons drift towards the anode and participate in ionization processes. The reason is the partial re-trapping of released surface electrons after subsequent back-diffusion to the dielectric.

Influence of laser photon energy
Since the laser photodesorption of surface electrons corresponds to an artificial increase in the SEE which enhances the pre-ionization, the BD mode might finally change. This was tested first for the laser wavelength l = 532 nm lsr which corresponds to the photon energy = E 2.33 eV ph . Figure 10 illustrates the laser photodesorption effect on the development of the glow-like BD, regarding the electrical characteristics in (a), and the spatio-temporal evolution of the He (    S  P  3  2   3 3 ) emission at l = 706.5 nm with laser pulse and without laser pulse in (b). As already discussed, the laser-induced effect is characterized by discrepancies in the ignition voltage, breakdown onset, and transported charge. The He line emission in figure 10(b) acts as an indicator for both high electron density and energy, since the resonantly excited He(3 S 3 ) state is dominantly populated by electron-impact excitation from the He ground state requiring high excitation energy of 22.7 eV, He 2 706.5 nm . 18 3 3 Both with and without laser pulse, the ionization front starts in front of the anode and propagates towards the cathode, as typical for the glow-like BD. However, the ionization front of the laser-affected discharge starts noticeably earlier and propagates slower compared to the unaffected development. This is due to the laser-induced decrease in breakdown voltage. But, the gap voltage drop during the laser-affected breakdown is still large, and the maximum emission is just slightly shifted towards the anode. Summarized, the discharge mode is not changed by laser photodesorption of surface electrons at = E 2.33 eV ph . This is confirmed by the simulated electrical characteristics and total ionization rate in figures 10(c) and (d). Releasing a surface electron density of s = --240 pC cm e tot 2 from the cathodic dielectric enhances the pre-ionization of the discharge in agreement with the experiment. As well, the reduced breakdown voltage causes a slower cathode-directed propagation of the ionization front and a decrease in total ionization rate during the breakdown phase. In contrast to the experiment, the simulation reveals a small additional current peak of sub-microsecond duration at the moment of the laser pulse. Since the amount of laser-released electrons is still below the detection limit of the measured total charge  . Note that this electron yield exceeds the total electron density deposited onto the dielectric surface. However, with consideration of the finite laser pulse duration and the effective re-trapping of released electrons, this is no contradiction. In agreement with the laser-affected discharge from experiment in figures 12(a) and (b), the gap voltage remains nearly constant and the discharge current is weak and long-lasting. As well, the total ionization rate is clearly enhanced during the pre-phase but reduced during the breakdown, and its maximum is shifted away from the cathode, see figures 12(c) and (d). Also, the additional current peak at the moment of the laser pulse is observed due the large amount of released surface electrons.

Stepwise release of surface electrons
In figure 13, the discharge current is plotted without and with laser photodesorption of surface electrons at = E 2.33 eV ph and = E 1.17 eV ph . The additional current peak caused by the released electrons just after the laser pulse at = E 1.17 eV ph is characterized by a raise to its maximum within few microseconds followed by a slightly slower decrease. This delay with respect to the moment of the laser pulse (10 ns duration) as well as the overall duration of this current peak take much too long compared to the transit time of electrons drifting through the 3 mm discharge gap when the breakdown voltage has been reached. Thus, the delay between the laser pulse and the current peak indicates the stepwise release of surface electrons initiated by the low laser photon energy. In fact, a reasonable microscopic description of an impure dielectric surface is beyond the scope of this work. However, one possible sequence for the stepwise electron release is shown in figure 14, which is a sketch of the interface between the discharge and the dielectric surface, based on the model in [16]. The bending of both the valence band and the CB is caused by the charging with surplus electrons. Most of the dielectric materials that are commonly used in BD configurations, such as silica or alumina, have positive electron affinity c > 0 [15]. The latter is defined as the energy difference between the lower edge of the CB and the effective surface potential wall just outside the dielectric boundary resulting from the superposition of the image potential and the plasma sheath potential. In this context, free electrons (Q free ) are defined as those electrons having enough energy to overcome the effective potential wall. In particular, the model in [16] predicts the trapping of electrons from the discharge within the CB, with subsequent relaxation to deeper energy levels. From experimental investigations of the thermally and optically stimulated luminescence [19,20], it is known that the residual surface electrons have low material-dependent binding energy in the order of 1 eV. Thus, the electrons are finally trapped in additional band gap states (Q gap ) originating from chemical contamination, doping, or structural damage caused by the discharge exposure.
In the present experiment using float glass plates covering the electrodes, it is therefore assumed that the laser photon energy = E 2.33 eV ph allows the direct release of surface electrons from the population Q gap . In contrast, the shape of the additional current peak using the low photon energy = E 1.17 eV  (22) is plotted as a dashed line in figure 13. In general, the calculated current reproduces the shape of the measured current peak induced by laser photodesorption at low photon energy = E 1.17 eV ph , which supports the assumption of stepwise electron release. In conclusion, at least two intermediate states for the surface electrons, here Q CB and Q SP , are necessary to explain (i) the delay between the laser excitation and the current pulse maximum, as well as (ii) the slow decrease afterwards. However, this simple 0D analytical calculation cannot perfectly match with the experiment due to spatial inhomogeneities in laser radiation intensity, and due to the lack of  knowledge about the underlying microscopic processes at the interface between the discharge volume and the dielectric surface.
Note that = -Q 0.7 nC e tot corresponds to4.4 10 9 released surface electrons. With consideration of the laser pulse energy = E 110 mJ lsr at the photon energy = E ph 1.17 eV used in the experiment, the total number of photons per laser pulse is about5.9 10 17 . Thus, the laser photodesorption efficiency defined as the ratio of released surface electrons to laser photons results in about 10 −8 , which seems to be very small. However, first of all, only the edge of the laser beam hits the dielectric surface, and the photon density is not constant across the axial laser beam profile but decreases significantly towards the edges. Secondly, the laser beam is only slightly divergent and, hence, nearly parallel to the dielectric surface, wherefore most of the photons become reflected there. Thirdly, due to the low photon energy, the laser can finally release only those surface electrons having a low binding energy.

Summary and outlook
The presented work studies the role of residual weakly-bound surface electrons for the pre-ionization in homogeneous glowlike helium BDs. A laser photodesorption experiment was performed and, in addition, a 1D numerical fluid simulation was set up to investigate the impact of released surface electrons on the discharge development. Both experiment and simulation revealed that releasing a small amount of surface electrons from the cathodic dielectric during the discharge pre-phase supports significantly the pre-ionization kinetics. As a result, the breakdown voltage is noticeably reduced which corresponds to an earlier discharge onset, the cathodedirected ionization front is slowed down, and the overall transported charge is less compared to the discharge without laser interaction. This result highlights the importance of weakly-bound surface electrons in acting as a seed electron reservoir for diffuse BDs driven by low operating frequency, as so far proposed in some simulations of the BD in helium and helium-oxygen mixtures.
In more detail, the axial laser beam position, the laser pulse time and energy, and the laser wavelength (photon energy) were systematically varied. Actually, the experiment verified that the surface electrons are weakly bound to the glass-coated electrodes, wherefore they can be released by laser at low photon energy of 2.33 eV. The comparison between experiment and simulation indicates that the laser photodesorption of surface electrons significantly supports the ionization kinetics at low background electron density in the gas volume. Only the released electrons from the cathodic dielectric are able to pass through the gas gap and participate in ionization processes. Both criteria are fulfilled during the discharge pre-phase, but neither during the breakdown nor during the post-phase.
Finally, the reduction of the laser photon energy from 2.33 to 1.17 eV causes an additional current peak just after the laser pulse, and the transition from the glow mode to the Townsend mode of the BD due to an effective increase in the secondary electron yield. The additional current peak caused by the large amount of released surface electrons reveals a remarkable delay to the short laser pulse. This can be explained by stepwise electron release initiated by laser excitation to a higher energy level within the dielectric. This approach is supported by analytical calculations based on a simple excitation sequence at the interface between the discharge and the dielectric surface.
To summarize, the investigations demonstrate the possibility to manipulate BDs by the laser interaction with charged dielectric-covered electrodes. Here, the binding energy of surface electrons was found to lie between 1.17 and 2.23 eV for the used float glass plate. Thus, the release of surface electrons by optical photons or thermal processes may essentially contribute to the pre-ionization of homogeneous BDs. The presented laser photodesorption effect is suitable to measure the binding energy of electrons deposited onto a dielectric surface, and to draw conclusions on effective SEE processes. For this purpose, it is planned to use tunable photon energies, and to investigate more well-defined dielectric materials, such as mono-crystalline silica, alumina, and magnesia. This intention should be combined with the direct measurement of surface electrons, e.g., based on the electro-optic Pockels effect of a Bi 12 SiO 20 crystal. Indeed, the effective SEE depends on the amount of surplus electrons adsorbed to the dielectric surface.