Blob interaction in 2D scrape off layer simulations
Gregor Decristoforo, Fulvio Militello, Odd Erik Garcia, Thomas Nicholas, John Omotani, Chris Marsden, Nick Walkden
BBlob interaction in 2D scrape off layer simulations
Blob interaction in 2D scrape off layer simulations
G. Decristoforo, a) F. Militello, b) O. E. Garcia, c) T. Nicholas, d) J. Omotani, b) C. Marsden, e) and N. Walkden b) (Dated: 9 July 2020) Interaction of coherent structures known as blobs in the scrape-off layer of magnetic confinement fusion devices isinvestigated. Isolated and interacting seeded blobs as well as full plasma turbulence are studied with a two dimensionalfluid code. The features of the blobs (size, amplitude, position) are determined with a blob tracking algorithm, whichidentifies them as coherent structures above a chosen density threshold and compared to a conventional center of massapproach. The agreement of these two methods is shown to be affected by the parameters of the blob tracking algorithm.The benchmarked approach is then extended to a population of interacting plasma blobs with statistically distributedamplitudes, sizes and initial positions for different levels of intermittency. As expected, for decreasing intermittency,we observe an increasing number of blobs deviating from size-velocity scaling laws of perfectly isolated blobs. This isfound to be caused by the interaction of blobs with the electrostatic potential of one another, leading to higher averageblob velocities. The degree of variation from the picture of perfectly isolated blobs is quantified as a function of theaverage waiting time of the seeded blobs.
I. INTRODUCTION
In tokamaks and other magnetically confined plasma exper-iments, particle transport in the plasma edge region is domi-nated by turbulence-driven coherent structures of high densityand temperature called blobs or filaments. This can lead tolarge erosion on the reactor walls and can contribute to thepower loads to divertor targets . These structures have beenobserved in multiple plasma devices in all operation regimesusing reciprocating or wall mounted Langmuir probes ,fast visual cameras and gas puff imaging .In addition to experimental evidence, theoretical understand-ing of the underlying physical mechanism of blob propaga-tion has been developed in the last 20 years . It is un-derstood that the basic mechanism responsible for the radialtransport of blobs arises due to grad-B and curvature driftsleading to a charge polarization in the plasma blob/filament.The resulting electric field gives rise to an E × B drift that pro-pels the blob across the magnetic field. Since detailed phys-ical models increase the analytical complexity significantly,the scientific community relies on numerical simulations ofisolated blobs and fully turbulent simulations of the scrapeoff layer. Numerical simulations in two dimensions andthree dimensions have enhanced the understanding of theunderlying mechanisms of blob and filament propagation inthe scrape off layer.Most of these numerical simulations investigate idealized iso-lated blobs modeled as positive symmetrical Gaussian per-turbations on a constant plasma background. This approachhas provided an effective way of investigating the influ- a) Electronic mail: [email protected] (corresponding author); De-partment of Physics and Technology, UiT The Arctic University of Norway,NO-9037 Tromsø, Norway b) CCFE, Culham Science Centre, Abingdon OX14 3DB, United Kingdom c) Department of Physics and Technology, UiT The Arctic University of Nor-way, NO-9037 Tromsø, Norway d) York Plasma Institute, Department of Physics, University of York, Hesling-ton, York YO10 5DD, United Kingdom e) University of Birmingham, School of Physics and Astronomy, Edgbaston,Edgbaston Park Road, Birmingham B15 2TT, United Kingdom ence of specific physical effects, such as finite Larmor ra-dius effects , electromagnetic effects or parallel electrondynamics on the blob velocity, coherence and lifetime. Scal-ing laws describing the radial blob velocity depending on it’samplitudes and size have been developed, and differentregimes determined by various physical parameters have beendiscovered .Despite this progress, understanding how well these scalinglaws describe blobs in fully turbulent scenarios where theyinteract with each other is non-trivial. Previous work hasshown that single blobs in close proximity do interact throughthe electric potential they generate . This analysis was per-formed on two spatially separated seeded blobs on a constantplasma background, and therefore does not address the com-plexity of a fully turbulent environment. In our work, we ex-pand the investigation by starting from isolated blob simula-tions and then extending our analysis to decreasingly inter-mittent systems, until we consider fully turbulent scrape-offlayer plasma. To bridge these two extremes we use a stochas-tic model of multiple randomly seeded blobs where blob am-plitudes, widths, initial positions and the waiting times be-tween consecutive blobs are randomly sampled from distribu-tion functions.In order to track blobs in these intermittent and turbulent sce-narios, we developed a new tool that allowed us to go beyondwhat was done in the past. Our blob tracking algorithm pro-vides specific parameters such as trajectory, velocity, size andamplitude over the lifetime of specific blobs. Tracking algo-rithms using either simple threshold methods, defining everycoherent structure above a chosen density threshold as a blob,or convolutional neural networks have been presented and ap-plied on two and three dimensional data . For our analy-sis we choose the threshold method, since it provides a simpleand consistent definition for blobs in the isolated and fullyturbulent case and is easy to implement. Applying blob track-ing techniques on experimental measurements on high speedimaging data using i.e. a watershed algorithm is compli-cated by the spatial and temporal resolution of the measure-ment techniques. This algorithm is based on fitting two di-mensional Gaussians to local density maxima in order to ex-tract the position, widths, amplitudes and positions of the fluc- a r X i v : . [ phy s i c s . p l a s m - ph ] J u l lob interaction in 2D scrape off layer simulations 2tuations.The structure of this publication is as follows: In section II wepresent the equations of the physical model that we use for ourfurther analysis. In section III we present a detailed descrip-tion of the implementation of the blob tracking algorithm anddiscuss all relevant parameters of this method. Furthermore,we apply this algorithm on isolated seeded blob simulationsin section IV and compare the results to a conventional cen-ter of mass approach. In section V we extend this analysison a model seeding multiple blobs randomly. We start withthe case of identical amplitudes and starting positions for dif-ferent intermittency parameters, extend this analysis to ran-dom initial positions and finally to a model including randomblob amplitudes. In all cases we compare the measurementsto the isolated blob simulations. In section VI we finally ap-ply the blob tracking algorithm on fully turbulent scrape offlayer simulations and discuss the results in comparison to theprevious models. II. PHYSICAL MODEL
For our analysis we choose a standard two dimensional(2D), two-field fluid model derived from the Braginskii fluidequations. We assume a quasi-neutral plasma, negligible elec-tron inertia, isothermal electrons, T e = constant, and cold ions, T i =
0. Note that these assumptions for the electron and iontemperatures are taken for the sake of simplification, as ex-perimental measurements of scrape off layer plasmas oftenshow high variations of T e and T i > T e . Nevertheless, thissimplified model still captures the fundamental dynamics ofthe blobs and is therefore sufficient to study their interactionwhile keeping the number of free parameters of the model rel-atively low.For our simulations, we use a simple slab geometry to modelthe plasma evolution perpendicular to the magnetic field, with x and y referring to the radial and the binormal/poloidal direc-tion. The normalized 2D electron particle continuity equationand vorticity equation take the form: dndt + g (cid:18) ∂ n ∂ y − n ∂ φ∂ y (cid:19) = D ⊥ ∇ ⊥ n + S n − λ ne − φ , (1) d ∇ ⊥ φ dt + gn ∂ n ∂ y = ν ⊥ ∇ ⊥ φ + λ (cid:0) − e − φ (cid:1) , (2)where n represents the plasma density, φ the electric poten-tial, g effective gravity, i.e. interchange drive from mag-netic curvature, S n the plasma source term and D ⊥ and ν ⊥ the collisional dissipative terms representing particle diffusiv-ity and viscosity. The parameter, λ is the parallel loss rateof the system. Note that the plasma source term S n only ap-pears for turbulence simulations and not for seeded blob sim-ulations. The standard Bohm normalization is used for thismodel equivalent to and is not discussed here for sake ofbrevity. In addition, we choose d / dt = ∂ / ∂ t + V E · ∇ ⊥ where V E = − ∇ ⊥ φ × B / B stands for the E × B drift. The last term on the right hand side of both the continuity and electron driftvorticity equation results from modelling the parallel losses tothe target.The numerical model is implemented in the STORM code which is based on BOUT++ . The code uses a finite dif-ference scheme in the x -direction and a spectral scheme inthe y -direction, time integration is performed by the PVODEsolver . We choose L x =
150 and L y =
100 with a resolutionof 256 ×
256 grid points for all runs. The coefficients are rep-resentative of a medium sized machine with g = . × − and λ = . × − . For single isolated blob simulations insection IV we choose D ⊥ = ν ⊥ = × − , while for the re-maining simulations of section V and VI D ⊥ = ν ⊥ = × − .We choose higher diffusion coefficients for isolated blob sim-ulations in section IV since the blob coherence stays higherfor higher diffusion coefficients. The source term for the tur-bulence simulations is S n = σ √ π e − ( x − µσ ) (3)with σ = µ =
30. The source term represents thecross field transport from the core region, but its magni-tude and shape here are arbitrary, although convenient. Wechoose periodic boundary conditions in the y -direction andzero gradient boundary conditions in the radial direction forboth the density and vorticity fields. For the plasma potentialwe choose fixed boundary conditions at the radial boundaries φ ( x = ) = φ ( x = ) = III. NUMERICAL IMPLEMENTATION OF BLOBTRACKING
The blob tracking algorithm is implemented in Python, em-ploying the xarray library . Blobs are identified as positivefluctuations above a certain density threshold. The optimalchoice of the thresholding technique depends on the problemat hand, and in the case of the isolated blob simulations pre-sented in Section IV, we take a constant threshold across thewhole domain. For the subsequent sections, however, we seta constant threshold on the density field, defined as the total n minus the y - and time averaged profile, as this method is morerobust for turbulence simulations due to the non-flat averageradial profile.We label the resulting coherent regions using the multi-dimensional image processing library scipy.ndimage . Notethat this implementation requires a relatively high temporalresolution of the output files since a blob is only labeled asone coherent structure over time, if the blob spatially overlapswith itself in the next frame. The downside of this approachis the resulting large output files, which slows down the mem-ory bound blob tracking algorithm. In addition, one has toconsider the periodic boundary condition in the y -direction,since the algorithm will label a blob traveling through the y -boundary of the domain as two different objects. For turbu-lence simulations in section VI, the blob tracking algorithm isonly applied in the domain region where x > . × L x , sincewe do not include the source term in our analysis. Remember,lob interaction in 2D scrape off layer simulations 3that the source term is not derived from physical quantities butserves as an artificial numerical term and would heavily inter-fere the labeling algorithm if included. From these labeledblobs it is straight forward to determine the center of mass ofeach blob at each time step, its trajectory, radial and poloidalvelocity, its amplitude, mass and size over time and its lifetime. We will use some of these blob parameters for our sta-tistical analysis for different models. We can then apply thismethod with the identical blob tracking parameters on isolatedblobs, statistically seeded blobs and fully turbulent scrape offlayer simulations in order to investigate how blob interactionis affected by the plasma intermittency, and its effect on theblob parameters.An example of the blob tracking and labeling methods appliedon a turbulence simulation is shown in figure 1. This figureshows the plasma density and the associated blobs detected byour algorithm for three different closely spaced frames. Theblob tracking further demonstrates in figure 1, how individu-ally, detected blobs propagate radially outwards and dissipateover time. IV. ISOLATED SEEDED BLOB SIMULATIONS
We begin the analysis by tracking single isolated blobs,seeded on a constant plasma background. We seed a sin-gle blob as a symmetrical Gaussian function with amplitude A and width δ at the initial position, x = . × L x and y = . × L y . The blob amplitude is set to be as large asthe plasma background, in this case A =
1. We perform a pa-rameter scan from δ = δ =
30 for the blob width. Theblob radial velocity is initially determined by subtracting theplasma background and using a center of mass approach forthe whole domain, in order to determine a reference which weuse to evaluate our implementation of the blob tracking algo-rithm. The x -component of center of mass of the single blobis therefore calculated by x cm ( t ) = (cid:82) dy (cid:82) x ( n ( x , y , t ) − n b ) dx (cid:82) dy (cid:82) ( n ( x , y , t ) − n b ) dx (4)where n stands for the evolving plasma density and n b for the plasma background density. The y -component iscalculated analogously and the velocity is determined by afinite difference scheme in time. Next, we determine theblob velocity by using the blob tracking algorithm for threedifferent thresholds. Our algorithm determines the radialvelocity of the blob by calculating the center of mass of theplasma region where the plasma density exceeds the thresholdand calculates the velocity again by a finite difference schemein time.The results of this analysis are shown in figure 2. For alldifferent methods of velocity measurements, we see that thesize-velocity dependence follows the theoretical scaling lawsstudied in previous work . These measurements showthat the calculated blob velocity is strongly dependent on thethreshold applied for the tracking. For a blob threshold ofonly one percent of its initial amplitude, we observe that themeasured velocity remains very close to the center of mass approach for all widths. This is not surprising, since thesetwo implementations are almost identical for low trackingthresholds. For higher blob thresholds, it is shown that thedetermined maximum radial velocity increases significantly,as the measured radial velocity for a threshold of 40 percentof the initial blob amplitude more than doubles the center ofmass results. This can be explained by the fact that for highthresholds the algorithm only detects the densest parts of theblob, that tends to propagate faster radially than their lessdense regions. This has to be taken into account for furtherwork when applying the blob tracking algorithm on morecomplex models than singular seeded blob simulations. δ ⊥ . . . . v x scaling lawsCOMBT BT BT FIG. 2. The dependence of the maximum radial velocity of isolatedseeded blobs on their widths compared to theoretical scaling laws.The blue dots refer to the center of mass approach, the other dots tothe blob tracking algorithm uses different percentages of the initialamplitude of the blob as a threshold. The radial velocity and the blobwidth is expressed in normalized units.
We further investigate how the blob velocity evolves overthe lifetime and how the results change for the different meth-ods. The results of this analysis are shown in figure 3 for arelatively small blob width of δ =
5. We observe the absolutevelocity dependence on the choice of the threshold of the al-gorithm. In addition, it is shown that the detected lifetime ofthe blob for a higher threshold is lower. This can be simplyexplained by the fact that a narrower blob dissipates energyfaster and its amplitude therefore falls under the threshold ofthe tracking algorithm. The precision of the blob trackingmeasurement also decreases with higher blob thresholds andsmaller blobs. Intuitively, the blob tracking algorithm showsthe best performance for wide blobs and low blob thresholds.Due to the good agreement between the results of the center ofmass approach and the blob tracking algorithm, we concludethat these methods are consistent, which motivates extendingour analysis to more complex models.
V. RANDOMLY SEEDED BLOB SIMULATIONS
The next step of our studies is a more complex model, inwhich blobs are seeded with random parameters, in partic-lob interaction in 2D scrape off layer simulations 4 x y t = 1250 . . . . . . . . . x y t = 1250 x y t = 1400 . . . . . . . . . x y t = 1400 x y t = 1550 . . . . . . . . . x y t = 1550 FIG. 1. Snapshots of plasma density n and associated blob labels from three closely spaced frames of a turbulence simulation with parametersequivalent to section II. x refers to the radial and y to the poloidal/binormal coordinate. The colorbar on the right represents the labelsof individual detected blobs. The source term on the left side of the domain is excluded from the blob detection algorithm. Radial blobpropagation and dissipation is shown for individual detected blobs. ular amplitude, width, initial poloidal/binormal launch posi-tion and waiting time between the launch of two consecutiveblobs. This model is still artificial but provides valuable in-sight in blob interaction in a controlled environment. We startour analysis by only keeping waiting times and widths as freeparameters and then gradually adding the remaining free pa-rameters to the model. In the most complex case we sam-ple the waiting times and amplitudes from an exponential dis-tribution and the initial poloidal/binormal starting positionsand the widths from a uniform distribution. Note, that we choose a uniform distribution for the widths for illustration,even though a log-normal or an exponential distribution wouldbe physically more accurate. Since we intend to compare thevelocity-size dependency of detected blobs in this model toisolated blob studies, we choose to sample from a uniformdistribution for the sizes to increase the number of big blobs.A snapshot of an example run of this model is shown in figure4 showing the density field of four seeded blobs with differ-ent widths and amplitudes. The blob at approximately y = . . . . . . . t × . . . . v x COMBT BT BT FIG. 3. Radial velocity of an isolated seeded blob width δ ⊥ =
5. Theblue line refers to the center of mass approach. The other lines referto the blob tracking algorithm using different percentages of its initialamplitude as the threshold. Radial velocity and time is expressed innormalized units. wards. The two blobs at approximately y =
50 show a stronginteraction between each other and merge eventually into onecoherent structure. A less intermittent case is shown in figure5 where individual blobs interact strongly with each other, re-sulting in a turbulence-like density snapshot.In the following analysis we choose the same parameters forour blob tracking algorithm for all runs, in order to keep com-parisons between different models consistent. In order notto overestimate the velocity of individual blobs one wouldchoose a relatively low threshold for the blob tracking algo-rithm. Nevertheless, the threshold cannot be set too low inthis model that simulates more than one blob since it wouldlabel several independent but spatially close structures as oneblob. We subtract the time and y -averaged radial profile fromthe density and apply a blob threshold of 0 . A. single launch-point
We begin our analysis on randomly seeded blobs, keepingthe blob amplitudes constant to A = x = . × L x and y = . × L y , which leaves the waitingtimes and blob widths as free parameters. In order to quantifythe interaction and overlap of individual blobs we define amodel specific intermittency parameter as I = (cid:104) v x (cid:105)(cid:104) τ w (cid:105)(cid:104) δ (cid:105) (5)where (cid:104) v x (cid:105) represents the average radial velocity, (cid:104) τ w (cid:105) the av-erage waiting time and (cid:104) δ (cid:105) the average width of a specific run.This model specific intermittency parameter is introduced inthe spirit of previous work on stochastic modeling of intermit-tent fluctuations, analyzing time series which defines theintermittency parameter as the ratio of the average duration x y . . . . . . . . . FIG. 4. Snapshot of plasma n of a simulation of randomly seededblobs with different amplitudes. x refers to the radial and y to thepoloidal/binormal coordinate. The blob at approx. y =
90 propagatesradially outwards without interfering with other blobs. At approx. y =
40 we see two blobs merging into one coherent structure. x y . . . . . . . . . . FIG. 5. Snapshot of plasma n of a simulation of randomly seededblobs with different amplitudes and low intermittency parameter. x refers to the radial and y to the poloidal/binormal coordinate. Weobserve strong interactions between individual seeded blobs similarto turbulence simulations. time of one event above a chosen threshold, and the averagewaiting time between two such consecutive events. From thedefinition I is, strictly speaking, not constant but a functionof δ of each individual blob. This effect is illustrated in fig-ure 6, showing how the blob specific intermittency parameterdeviates from the average value. This has to be taken intoconsideration for the following investigation. Note, that forthe presented cases we calculate (cid:104) v x (cid:105) and (cid:104) δ (cid:105) not from inputparameters of the model but from the set of seeded blobs ex-cluding structures that only are detected for one frame. Welaunch blobs for three different average waiting times whichrefer to three different states of intermittency. The results ofthe blob tracking algorithm for these three cases are shown infigure 7.Note that the width δ of the blobs shown in figure 7 is de-termined by the blob tracking algorithm and does not exactlymatch the values of the input parameters. For the most inter-lob interaction in 2D scrape off layer simulations 6 δ I scaling lawsaverage FIG. 6. Model specific intermittency parameter in dependence ofblob width illustrated utilizing scaling laws for the inertial (small δ )and sheath connected blob regime (big δ ). This is compared to theaverage intermittency parameter for all δ . mittent case of I = .
8, where blobs are the most spatiallyseparated, we see that the overwhelming majority of detectedstructures lies on the line of isolated blobs. This implies thatthere is no strong interaction between individual blobs. Someindividually detected structures show a higher radial velocitythan their isolated counterparts. This effect arises due to twoclosely separated blobs interacting with each other’s electro-static potential. Although this has been studied in some detailin previous work , we deliver an illustration in figure 8. Weseed two identical blobs at different radial positions and applythe blob tracking algorithm to determine their radial velocity.The electrostatic potential created by the two separate blobssuperposes and results in a stronger electric filed which in-creases the E × B drift that drags the coherent blob structuresradially outwards. This effect leads to the formation of socalled "blob trenches" in turbulence simulations. We measureradial velocity of the two blobs with the blob tracking algo-rithm and observe a clear increase in velocity for the secondblob, shown in figure 9.For I = . I = . B. random launch-point
The next free parameter of the investigated model added toour analysis is the poloidal/binormal launch position of theseeded blobs. We sample the launch position y from a uni-form distribution U ( . × L y , . × L y ) to avoid blobs propa-gating through the poloidal/binormal boundaries. The ampli-tudes remain as the last fixed parameter set to A =
1. Seedingblobs from a random poloidal/binormal position increases theintermittency of the model and leads to more complex interac-tions between individual structures. We therefore multiply theexpression for the intermittency parameter shown in equation6 with L y / (cid:104) δ (cid:105) resulting in I = (cid:104) v x (cid:105)(cid:104) τ w (cid:105) L y (cid:104) δ (cid:105) (6)to consider this extension of the model, since L y / L y . We run this modelfor three different intermittency parameters and present thedetected blobs in figure 10. As one might expect, mostdetected structures in the I = . A = C. different amplitudes
We add the last free parameter of our model by seedingblobs with exponentially distributed amplitudes. From thesampled amplitudes we only choose those with 0 . < A < δ . . . . . v x seededisolated δ . . . . . v x seededisolated δ . . . . . v x seededisolated FIG. 7. Radial velocity of randomly seeded blobs with single launch position (blue dots) compared to isolated blobs (orange dots). Theintermittency parameters for the displayed runs are approximately I = . I = . I = . δ ∈ U ( , ) and waiting times from an exponential distribution. lated seeded blobs with amplitudes A = . A = VI. TURBULENT SIMULATIONS
After investigating randomly seeded blob models, we turnour attention to a simple self consistent scrape off layer modelsimulating plasma turbulence. Numerically, the model staysequivalent to the seeded blob simulations but uses the termof equation 3 as a plasma source instead of Gaussian seededblobs. The density profile in the simulation domain are builtand balanced by the plasma source and the sheath dissipationincluded in the model. These are unstable due to bad curvatureand interchange instability, which leads to coherent structuresof plasma propagating radially outwards due to the blob mech-anism discussed in the introduction. These blob like structuresvary in amplitude and width and can be detected and trackedby the tracking algorithm.We exclude the source term for our blob tracking analysisand only consider coherent structures detected at x > . × L x since this unphysical term only serves as a numerical term.In addition, we only include blobs with an initial center ofmass of 0 . × L y < x init < . × L y in our statistical evalu-ation in order to exclude distorted tracked structures becauseof the periodic boundary conditions in the y -dimension. Eventhough it is straightforward to track blobs consistently that tra-verse the simulation border in this direction, our numerical implementation for this issue is computationally more expen-sive than running the simulation longer, and only consideringblobs in the central band of the domain. For such turbulencesimulations the tracking algorithm identifies numerous smallstructures that only appear for one frame. These structuresrepresent approximately one third of the total number of de-tected blobs and are also excluded in our statistical analysis.The remaining parameters for the tracking algorithm stay thesame as for the randomly seeded blob model. The determinedradial velocities and sizes of the detected blobs in the turbu-lence simulation are shown as a 2D histogram in figure 14. Wechoose this type of plot since the illustrated 4542 blobs are toomany to be shown distinctively in a scatter plot. The distribu-tion of the sizes and amplitudes of the detected structures, aswell as the joint probability distribution functions (PDF) ofthese two blob parameters, are shown in figure 15.These measurements show that the amplitudes lie in between A = .
2, which is equivalent to the threshold used for the blobtracking algorithm, and A = .
7. Since blobs with an ampli-tude smaller than A = . A = . ρ = .
85. In orderto compare the detected blobs with their isolated counterpartswe perform a parameter scan for blobs with the amplitudes A = . A = . A = . A = . δ ⊥ =
30 appear,therefore we rarely observe the decreasing radial velocity forbigger and denser blobs in our velocity-size scaling. Never-theless, the data set provides enough information to discussthe results in comparison to isolated blob simulations. As inthe previous model of randomly seeded blobs with randomamplitudes, we observe that the overwhelming majority of de-tected blob structures lie in between the trends of the isolatedlob interaction in 2D scrape off layer simulations 8 t = 25 t = 25 t = 750 t = 750 t = 1250 t = 1250 FIG. 8. Snapshot of two seeded identical blobs with their electrostatic potential and the associated blob labels, detected by the blob trackingalgorithm at three different time steps. The acceleration of the left blob by the electrostatic potential of the right blob is illustrated. blob simulations. As for the previous model, the algorithmdetects a significant number of structures with a higher radialvelocity than the isolated blobs. We explain these events againby the interaction of blobs with the electrostatic potential ofone another. Due to these findings we conclude that trackingblobs in a fully turbulent scenario shows very similar resultsto models of statistically seeded blobs. While the theoreticalsize-velocity scaling of isolated blobs gives a reasonable or-der of magnitude estimate, there is an order unity scatter dueto strong interactions between blobs.
VII. DISCUSSION AND CONCLUSION
In this work we investigated the interaction of blobs in thescrape-off layer for different models of varying complexity.In particular, we compared the relation between the radialvelocity and the widths of the blobs with established scalinglaws. We started with studying isolated blob and extendedour analysis on a model of randomly seeded blobs where theparameters are sampled from physically adequate PDFs. Westudied this model for different levels of intermittency andapplied the acquired knowledge on fully turbulent scrape offlayer plasma simulations.In this process we developed a blob tracking algorithmas a versatile tool to analyze and understand blob andlob interaction in 2D scrape off layer simulations 9 . . . . . . . t × . . . . v x Blob 1Blob 2
FIG. 9. Radial velocity of two seeded identical blobs at two differentradial positions. Blob 2, which is trailing blob 1, shows a significantincrease in the radial velocity due to the electrostatic potential createdby blob 1. plasma parameters in scrape off layer plasma simula-tions. We publish our implementation on github underhttps://github.com/gregordecristoforo/xblobs.. The currentimplementation is only valid for STORM simulations butmodifying the algorithm for general BOUT++, or othersimulations using xarray to manage their output files, isstraightforward. An extension of the algorithm to threedimensions is numerically easy to implement, but the 2Dversion of this algorithm can be valuable for analyzing blobpropagation and turbulent transport, in a specific plane inthree dimensional plasma simulations. We will use this inthe future to study how blob properties depend on specificphysical effects or study the plasma transport in the scrape offlayer.We observe an increase of the radial velocity for blobs incases of low intermittency for the randomly seeded blobmodel and turbulence model, compared to isolated and inter-mittent cases. We explain this observation by the interactionof blobs with the electrostatic potential of one another. Theblob trajectories are influenced by the electrostatic potentialwhich gets diverted, leading to the creation of trenches inwhich blobs get accelerated by the potential of ones in frontof them. These findings are consistent with previous workstudying the interaction of two seeded blobs . Unsurpris-ingly, a decrease in intermittency of the studied model showsan increase of spread in the size-velocity relation of theblobs. For all studied models we still observe a clear trendin the size-velocity relation. This concludes that despite thesignificant interaction of blobs, they still follow establishedscaling laws and can therefore be regarded to lowest order,as isolated structures propagating radially through the scrapeoff layer. We thereby display the relevance of isolated seededblob and filament simulations for complex turbulent models. ACKNOWLEDGEMENTS
This work was supported with financial subvention from theResearch Council of Norway under grant 240510/F20. GDacknowledges the generous hospitality of the Culham Centrefor Fusion Energy (CCFE) where this work was conducted.In addition, this work has been partially funded by the EP-SRC Grant EP/T012250/1 and partially carried out within theframework of the EUROfusion Consortium and has receivedfunding from the Euratom research and training programme2014-2018 and 2019-2020 under grant agreement No 633053.The views and opinions expressed herein do not necessarilyreflect those of the European Commission. The MARCONIsupercomputer was used for parts of the computational workunder the project number FUA34_SOLBOUT4.
DATA AVAILABILITY
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