Plasma Density Profile Research Articles

Combined plasma lens and rephasing stage for a laser wakefield accelerator

Electrons from a laser wakefield accelerator have a limited energy gain due to dephasing and are prone to emittance growth, causing a large divergence. In this paper, we experimentally show that adjusting the plasma density profile can address both issues. Shock-assisted ionisation injection is used to produce 100 MeV quasi-monoenergetic electron bunches in the primary part of the accelerator. Downstream from the accelerator, a second, independently tuneable density region is added, which can be used to either boost the energy of the electron bunches or as a plasma lens for significant divergence reduction. An additional energy gain of 25% and a 40% divergence reduction are obtained. Theoretical models validate the effects.

Guiding properties of Bessel–Gaussian and super-Gaussian pulses in inhomogeneous parabolic plasma channels

The guidance and stable propagation of laser pulses over many Rayleigh lengths are crucial for the plasma electron acceleration in the laser wakefield accelerators. Using plasma channels with specific characteristics can lead to the proper guidance of the laser pulse. Here, quasi-three-dimensional particle-in-cell (PIC) simulations are performed to investigate the guidance of Bessel–Gaussian pulse (BGP) of zeroth order and super-Gaussian pulse (SGP) of 3rd and 4th orders in an axially and radially inhomogeneous plasma channel. The effects of the channel radius and depth, the laser wavelength and initial spot size, and the plasma channel inhomogeneity on the guidance of the laser pulse are also examined. The results indicate that the guidance of a laser pulse in the plasma channel depends on the pulse profile, and under certain conditions, the pulses can be guided with the least variation of spot size in the inhomogeneous plasma channel. It is shown that the channel depth and the initial laser spot size are very effective in pulse guiding, as the values of these parameters increase, the pulse guidance is done better. In addition, the results show that the guidance of laser pulse is dependent on the type of plasma inhomogeneity represented by three different kinds of initial conditions, as considering the nonlinear-axial inhomogeneity in the parabolic plasma channel can lead to more convergence than the axially homogeneous and linear-axially plasma density profiles.

Frequency linearization of voltage controlled oscillator (VCO) for 2 µs frequency modulated continuous wave (FMCW) reflectometer.

Frequency modulated continuous wave reflectometers have been widely used to measure plasma density profiles in many magnetic fusion devices. The frequency modulation (FM) time of the KSTAR reflectometer was 20 µs, that is, the FM rate was 50kHz. However, the edge density of the KSTAR tokamak fluctuates typically over the frequency range of 20-50kHz in the ELMy H-mode plasmas. Therefore, the density profile changes significantly during the FM time, causing significant distortion in the density profile measurements. The FM rate must be increased at least ten times faster than the density fluctuation frequency. A new voltage controlled oscillator (VCO) driver is designed based on the AD8067 operational amplifier to achieve a FM time of 2 µs. The VCO output frequency is linearly modulated by predistorting the tuning voltage of VCO using a 400 MSamples/s arbitrary waveform generator. The resulting output frequency of the VCO is measured by mixing the VCO output with a fixed frequency synthesizer signal and measuring the mixer intermediate frequency using a 2.5 GSamples/s digitizer. The tuning voltage is adjusted to minimize the amount by which the measured frequency deviates from the linearly modulated frequency. A simple linear adjustment proportional to the deviation does not effectively suppress the nonlinearity in FM. The response time of the VCO driver and the VCO input interface should be taken into account by solving the entire circuit equation. In this paper, the developed VCO driver circuit and the frequency linearization method are described.

Classification of the L-, H-mode, and plasma-free state: Convolutional neural networks and variational autoencoders on the edge reflectometer for KSTAR.

Classifying and monitoring the L-, H-mode, and plasma-free state are essential for the stable operational control of tokamaks. Edge reflectometry measures plasma density profiles, but the large volume of data and complexity in reconstruction pose significant challenges. There is a need for efficient methods to analyze complex reflectometer data in real-time, which can be addressed using advanced computational techniques. Here, we show that machine learning (ML) techniques can classify discharge states using raw signal data from an edge reflectometer installed on the Korea Superconducting Tokamak Advanced Research. The deep convolutional neural network models achieved classification accuracy of up to 99% when using 2D spectrogram inputs, demonstrating a significant improvement over 1D raw signal inputs. Additionally, the variational autoencoder model effectively clustered the discharge states in the latent space without any label information, further validating the model's capability to classify discharge states. These results suggest that the ML model can effectively handle the complexity of reflectometer data and accurately classify plasma discharge states. This approach not only facilitates real-time diagnosis but also reduces the need for manual data processing.

Density-profile imaging using a second harmonic dispersion interferometer configured with reflective-beam expanders.

A Second-Harmonic Dispersion Interferometer (SHDI) is assembled to measure the two-dimensional, line-integrated density profile of a pulsed-plasma jet using probe-beam diameters well beyond the 1mm diameters typically used in such instruments. An initial prototype demonstrated the technique using 7mm beam diameters, which are now increased to 35mm diameter using two types of beam expanders: an achromatic-beam expander (ABE) or a reflective-beam expander (RBE). ABEs were found to add a periodic background to the measured-phase image with a magnitude of the order of Δϕ ∼ 2π radians, compared to the background phase noise level in the system configured without beam expanders at Δϕbg ∼ 0.025 radians. Subtraction of the background phase in a sample image reduced the effect of the ABE phase offset to a level of Δϕ ∼ 0.1 radians, enhancing the quality of the density measurements. Reflective-beam expanders (RBEs) did not modify the background phase appreciably and were a significant improvement, allowing the instrument to be used for 2D (r, z) density-profile measurements of a 3cm diameter × 5cm long, pulsed-plasma jet. Variations in the timing parameters for the plasma gun, specifically the gas valve opening time and the gas-injection delay, for a constant discharge current were used to map the plasma gun's performance, indicating a nominal line-integrated electron density of Nedl ≳ 3 × 1015 cm-2 and a volumetric density of Ne ≃ 9 × 1015cm-3. The results obtained for the RBE configuration demonstrate that the 2D-SHDI platform may be scaled to even larger sample areas and a rep-rated system, with the ability to potentially provide for a reproducible, time-resolved (∼1 ns), high resolution (∼100μm) measurement of 2D plasma-density profiles.

Effect of gas injection pattern on magnetically expanding rf plasma source

Abstract Argon gas is injected from a back plate having either a radial center hole or shower-patterned eight holes into a 13.3-cm-diameter and 25-cm-long radio frequency (rf) plasma source attached to a 43.7-cm-diameter and 65cm-long diffusion chamber under an expanding magnetic field, which resembles the magnetic nozzle rf plasma thruster. The source has a double-turn loop antenna powered by a 13.56 MHz rf generator at a maximum power level of ~2.8 kW in low-pressure argon, providing a plasma density of about 1018 m−3 in the source. A high plasma density and a slightly low electron temperature are obtained for the shower-pattered case in both the source tube and the diffusion chamber, compared with the center hole case, suggesting that the neutral density profile significantly affects the plasma density profile. This result will provide an improvement in the thruster performance by the gas injection pattern.

Direct laser acceleration in varying plasma density profiles

Abstract Direct laser acceleration has proven to be an efficient source of high-charge electron bunches and high brilliance x-rays. However, an analytical description of the acceleration in the interaction with varying plasma density targets is still missing. Here, we provide an analytical estimate of the maximum energies that electrons can achieve in such a case. We demonstrate that the maximum energy depends on the local electron properties at the moment when the electron fulfills the resonant condition at the beginning of the acceleration. This knowledge enables density shaping for various purposes. One application is to decrease the required acceleration distance needed to achieve the maximum electron energy. Another use for density tailoring is to achieve acceleration beyond the radiation reaction limit. We derive the energy scaling law that is valid for arbitrary density profile that varies slowly compared with the betatron period. Our results can be applied to electron heating in exponential preplasma of thin foils, ablating plasma plumes, or gas jets with long-scale ramp-up.

Particle transport in reduced turbulence neutral beam heated discharges at Wendelstein 7-X

A spontaneous reduction in anomalous particle transport in the plasma core is seen experimentally in reproducible, purely neutral beam heated plasma phases at Wendelstein 7-X (W7-X). Heating and fueling the plasma exclusively with the neutral beam injection system for several seconds leads to continuously peaking plasma density profiles with strong gradients inside mid minor radius. A significant acceleration of the density peaking occurs after a certain onset time and is examined with a detailed particle transport analysis in several discharges. By invoking the particle continuity equation, the total experimental radial electron flux is deduced from the time evolution of the electron density profile and the radially resolved particle sources. Subtracting the modeled neoclassical particle flux contribution gives the anomalous particle flux. Exploiting the evolving plasma conditions, anomalous diffusion and convection coefficients are computed from the flux variation with density and density gradients. In several discharges a significant and consistent change of the anomalous transport coefficients is seen when crossing a specific normalized density gradient length.

Benchmarking of hydrodynamic plasma waveguides for multi-GeV laser-driven electron acceleration

Hydrodynamic plasma waveguides initiated by optical field ionization have recently become a key component of multi-GeV laser wakefield accelerators. Here, we present the most complete and accurate experimental and simulation-based characterization to date, applicable to current multi-GeV experiments and future 100 GeV-scale laser plasma accelerators. Crucial to the simulations is the correct modeling of intense Bessel beam interaction with meter-scale gas targets, the results of which are used as initial conditions for hydrodynamic simulations. The simulations are in good agreement with our experiments measuring evolving plasma and neutral hydrogen density profiles using two-color short pulse interferometry, enabling realistic determination of the guided mode structure for application to laser-driven plasma accelerator design. Published by the American Physical Society 2024

Role of radiation re-absorption in the thermal helium beam diagnostic.

The Thermal Helium Beam (THB) is a diagnostic for simultaneously measuring the electron temperature and density profiles of the plasma edge and scrape off layer (SOL). It exploits the line ratio technique of selected He line intensities, emitted by He gas puffed inside the plasma, to locally estimate the plasma properties through a dedicated collisional radiative model (CRM). Standard THB diagnostics used in nuclear fusion devices measure three HeI emission lines: 667.8, 706.5, and 728.1nm. For the RFP experiment RFX-mod2, a new THB is designed and tested for the first time at the TCV tokamak. It acquires an additional emission line at 501.6nm, which is exploited to estimate the radiation re-absorption, which is not negligible in regions of large neutral He densities (leading to high re-absorption) and simultaneously low electron density and temperature (lack of other excitation channels). It affects the measurements most strongly at the far SOL, while the significance of re-absorption decreases as it approaches the separatrix. In this paper, plasma density and temperature profiles of the plasma edge at the outboard midplane of TCV, measured with this newly designed THB, are presented. For the first time, the effect of radiation re-absorption on the estimation of electron temperature and density profiles is experimentally measured in a tokamak using the 501nm line emission intensity. Different CRMs are compared with and without radiation re-absorption, showing good agreement when re-absorption is included and demonstrating how it plays an important role in the far SOL, as expected.

Gyrokinetic simulations of electrostatic microturbulence in ADITYA-U tokamak with argon impurity

The effect of impurity on the electrostatic microturbulence in ADITYA-U tokamak is assessed using global gyrokinetic simulations. The realistic geometry and experimental profiles of the ADITYA-U are used, before and after argon gas seeding, to perform the simulations. Before the impurity seeding, the simulations show the existence of the trapped electron mode (TEM) instability in three distinct regions on the radial-poloidal plane. The mode is identified by its linear eigenmode structure and its characteristic propagation in the electron diamagnetic direction. The simulations with Ar1+ impurity ions in the outer-core region show a significant reduction in the turbulence and transport due to a reduction in the linear instability drive, with respect to the case without impurity. A decrease in particle and heat transport in the outer-core region modifies the plasma density profile measured after the impurity seeding. It, thus, results in the stabilization of the TEM instability in the core region. Due to the reduced turbulence activity, the electron and ion temperatures in the central region increase by about 10%.

Effect of electron and ion mobility on edge biasing in tokamak plasmas

We present an improved model for the study of edge biasing in a tokamak plasma that incorporates electron and ion mobility contributions. The non-ambipolar nature of the drifts due to the electron/ion mobility terms influences the space charge separation due to edge biasing and affects plasma dynamics in the edge and SOL regions in a significant manner. In contrast to earlier studies, the present model enables simulation studies at higher biasing voltages. The inclusion of mobility enhances/decreases the effect of negative/positive biasing. The radial profiles of plasma density, electron temperature, radial electric field, and its shear for positive as well as negative biasing are investigated as a function of mobility.

Effect of trapezoidal plasma density region in bubble wakefield acceleration

In the process of bubble wakefield acceleration highly nonlinear region is developed inside plasma, which intuitively suggests that nonuniform plasma density having gradients may be more suited to achieve large nonlinearity in the system. Moreover, when an intense laser pulse propagates in a plasma, it is subjected to various instabilities and these instabilities can be controlled by plasma density profiles which effectively control the energy and flux of the accelerated particles. Considering all these points we investigate in the present work the scaling effect of up-ramp and down-ramp regions in plasma density profile on the bubble wakefield. These regions are separated by a plateau region (maximum density) enabling the density to have trapezoidal profile. With this density profile, the bubble wakefield acceleration is examined considering four different lengths of up-ramp and plateau regions keeping a constant down-ramp length. Increasing steepness of up-ramp length (larger density gradient), i.e., lowering the length of up-ramp and increasing the plateau length creates a bubble having higher wakefield strength, resulting into higher accumulation of plasma electrons at its tail and higher energy spectrum with higher kinetic energy gradient and Poynting flux of accelerated electrons.

Large-amplitude plasma wave generation by laser beating in inhomogeneous magnetized plasmas

Large-amplitude plasma wave is known to accelerate electrons to high energies. The electron energy gain mainly depends on plasma wave amplitude. In this paper, we investigate the excitation of large-amplitude plasma waves by laser beat-wave in an inhomogeneous plasma. The idea behind this work is to employ linear and radial plasma density profiles to enhance the plasma wave amplitude. PIC simulations are used to validate the numerical solution of the nonlinear wave equation in cylindrical dimensions through the finite difference method. Furthermore, the effects of the quadratic-radial plasma density profiles and magnetic field on the plasma wave excitation are investigated. The study shows that compared to the linear density profile of plasma, the plasma wave amplitude in the case of a linear-radial density profile is far more pronounced. For the linear-radial density profile, the plasma wave amplitude remains steady over greater distances of propagation compared to the linear density profile, resulting in reduced immediate damping effects. It can also be seen that the plasma wave amplitude is higher for the quadratic-radial than for the linear-radial density profiles. The effect of a longitudinal magnetic field on plasma wave amplitude is investigated. It can be seen that the plasma wave amplitude is increased by applying a magnetic field. This study may provide a way to enhance the plasma wave field for accelerating the electrons in laser-plasma accelerators.

Simultaneous measurement of surface velocity and plasma density with interferometric velocimetry.

The apparent velocity measured by an interferometric surface velocimeter is a function of both the surface velocity and the time derivative of the refractive index along the measurement path. We employed this dual sensitivity to simultaneously measure km/s surface velocities and 1018cm-3 average plasma densities with combined VISAR (velocity interferometer system for any reflector) and PDV (photonic Doppler velocimetry) measurements in experiments performed on the Z Pulsed Power Facility. We detail the governing equations, associated assumptions, and analysis specifics and show that the surface velocity can be extracted without knowledge of the specific plasma density profile.

Suppression of equilibrium magnetic islands by density profile effect in quasi-axisymmetric stellarator plasmas

In a quasi-axisymmetric stellarator, a significant bootstrap current will result in the generation of low-order rational surfaces and three-dimensional (3D) magnetic islands. In this paper, the influence of plasma density profiles on the equilibrium magnetic islands for the Chinese first quasi-axisymmetric stellarator (CFQS) is investigated using the HINT code. It is found that the flattening of the core plasma density profile leads to a significant suppression of magnetic islands. When the peaking factor of plasma density is 1.19, complete suppression of magnetic islands occurs while maintaining excellent integrity of the magnetic surface even with the volume-averaged plasma beta <β> increase up to 2%. On the other hand, during the transition of a plasma density profile from flat to hollow, there is a reversal in the core bootstrap current, resulting in reduction of rotational transform values to pass through the rational surface. Hence, formation of magnetic islands in the core region. Therefore, effective inhibition of CFQS’s magnetic islands can be achieved by appropriately controlling density profiles through methods like gas injection.

Role of gas composition in weakened nonlinear standing wave excitation and improved plasma radial uniformity in very-high-frequency asymmetric capacitive Ar/CF4 discharges

The higher harmonics generated by nonlinear sheath motion would enhance the standing wave effect, and thus lead to center-peaked plasma density profile in very-high-frequency (VHF) capacitive discharges. In this work, a nonlinear transmission line (NTL) model introduced in Zhou et al (2021 Plasma Sources Sci. Technol. 30 125017) has been extended, with radial transport of various particles and nonlinear sheath motion into account, to investigate the effects of CF4 fraction α on the nonlinear standing wave excitation and plasma radial uniformity in VHF (60 MHz) capacitively coupled Ar/CF4 plasmas at 3 Pa. The results indicate that for pure Ar discharges (i.e. α= 0%), the nonlinearly excited harmonics with short wavelength significantly enhance the electron power absorption at the radial center, resulting in a pronounced central-high plasma density profile. As α increases, the high-order harmonics are gradually damped due to the increase of resistance, as well as the longer wavelength caused by thicker sheath thickness. Thus, the radial profile of the electron absorbed power density shifts from center-peak to edge-high. Besides, at the radial center, the electron density and Ar+ ion density decrease with α , CF3 + ion density shows an increasing trend, while F− ion density initially rises and then decreases. Moreover, the density profiles of all the species become more uniform at higher CF4 fraction, due to the suppressed nonlinear standing wave excitation and the longer wavelength of the nonlinear harmonics.

Evaluation of H-/D- Density Using Langmuir Probe Measurement in a Cs Seeded Negative Ion Source

An electron reduction model is reintroduced for Langmuir probe plasma density profile measurement. The model is compared with conventional laser photo-detachment measurements and can predict negative ion density in the 2-3 x 1017m−3 range using correlation factors for hydrogen and deuterium cases. The calibration and correction procedure is demonstrated for application to ion sources.

Effect of antenna helicity on discharge characteristics of helicon plasma under a divergent magnetic field

The characteristics of the blue core phenomenon observed in a divergent magnetic field helicon plasma are investigated using two different helical antennas, namely right-handed and left-handed helical antennas. The mode transition, discharge image, spatial profiles of plasma density and electron temperature are diagnosed using a Langmuir probe, a Nikon D90 camera, an intensified charge-coupled device camera and an optical emission spectrometer, respectively. The results demonstrated that the blue core phenomenon appeared in the upstream region of the discharge tube at a fixed magnetic field under both helical antennas. However, it is more likely to appear in a right-handed helical antenna, in which the plasma density and ionization rate of the helicon plasma are higher. The spatial profiles of the plasma density and electron temperature are also different in both axial and radial directions for these two kinds of helical antenna. The wavelength calculated based on the dispersion relation of the bounded whistler wave is consistent with the order of magnitude of plasma length. It is proved that the helicon plasma is part of the wave mode discharge mechanism.

Bayesian inference of electron density and ion temperature profiles from neutral beam and halo Balmer-α emission at Wendelstein 7-X

By employing Bayesian inference techniques, the full electron density profile from the plasma core to the edge of Wendelstein 7-X (W7-X) is inferred solely from neutral hydrogen beam and halo Balmer-α (Hα) emission data. The halo is a cloud of neutrals forming in the vicinity of the injected neutral beam due to multiple charge exchange reactions. W7-X is equipped with several neutral hydrogen beam heating sources and an Hα spectroscopy system that views these sources from different angles and penetration depths in the plasma. As the beam and halo emission form complex spectra for each spatial point that are non-linearly dependent on the plasma density profile and other parameters, a complete model from the neutral beam injection and halo formation through to the spectroscopic measurements is required. The model is used here to infer electron density profiles for a range of common W7-X plasma scenarios. The inferred profiles show good agreement with profiles determined by the Thomson scattering and interferometry diagnostics across a broad range of absolute densities without any changes to the input or fitting parameters. The time evolution of the density profile in a discharge with continuous core density peaking is successfully reconstructed, demonstrating sufficient spatial resolution to infer strongly shaped profiles. Furthermore, it is shown as a proof of concept that the model is also able to infer the main ion temperature profile using the same data set.