# Density Limit In Tokamaks

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### Fusion Energy Sciences Progress on Disruption Event

PPPL TSDW 2018: Progress on Disruption Event Characterization and Forecasting in Tokamaks (S.A. Sabbagh, et al. 7/16/18) 11 DECAF density limit analysis started: global, local density limits examined, correlation of MHD onset near limits Disruptivity vs. density DIS Magnetic spectrogram (toroidal array) Greenwald limit

### The H-mode density limit in the full tungsten ASDEX Upgrade

The H-mode density limit in the full tungsten ASDEX Upgrade tokamak 3 Figure 3. Line integrated edge density plotted versus the neutral gas pressure in the divertor as shown in Figure 2. The plasma density saturates and reaches a fueling limit (red line). C. Evolution of a typical HDL gas ramp discharge Figure 4.

### Density limits in toroidal plasmas

even when far from the disruptive limit. Plasma density would seem to be bounded by two limits, both of which are proportional to plasma current density. In the absence of ﬁeld errors which can cause locked modes and reduce the accessible operational range, the low-density limit for tokamaks and RFPs sets in at about 5 10% of the high

### On the Origin of Current Scaling in the Density Limit

On the Origin of Current Scaling in the Density Limit P.H. Diamond, R. Singh, M. Malkov, R. Hajjar+ U.C. San Diego, USA APS 2019 + Present Address: General Atomics

### The$Tokamak$Density$limit:$a Thermoresisve $Disrup2on$Mechanism$

Jul 15, 2015 The$Tokamak$Density$limit:$a Thermoresisve $Disrup2on$Mechanism$ Presented$by$D.$A.$Gates$ In$collaboraon$with$ D.P.Brennan,$L.$DelgadoDAparicio,Q.$ Teng,$R.$B.$White$

### INVESTIGATION OF PHYSICAL PROCESSES LIMITING PLASMA DENSITY

accessed in which density - 1.5 x Greenwald limit was achieved for 600 ms, and good H-mode confinement was maintained for 300 ms of the density flat- top. More significantly, the density was successfully increased to the limit where a central radiative collapse was observed, the most fundamental density limit in tokamaks.

### DISRUPTION EVENT CHARACTERIZATION EX/P6-26 AND FORECASTING IN

limit in tokamaks, including a ballooning stability limit at the separatrix [8] and a local island power balance theory [9,10]. In the latter theory, power balance in an island between input Ohmic heating and radiated power loss results in a maximum local density that scales with local current density. If the density at the island exceeds

### EDGE TURBULENCE AND TRANSPORT AS A POSSIBLE CAUSE OF THE

density limit in tokamaks does not depend strongly on input power x x x x x + + + 12 10 divertor ip = 0.5 1.9 ma bt = 0.8 2.1 t a

### 1 Topic: CT/P-04 by J. A. Snipes

Now, this low density limit has been adjusted for each machine. The new fits for these 9 tokamaks are (660 points): P =1.67 ±0.30

### Zonal Flow and Zonal Magnetic Field Generation by Finite b

MHD below the ideal limit, the anomalous trans-port from resistive ballooning modes is very large and in-creases with a MHD. They interpret the computed large levels of transport to be responsible for the density limit in tokamaks. However, for ﬁnite a D,asa MHD is increased, there is a transition from a poorly conﬁned state (L mode)

### A New Look at Density Limits in Tokamaks

While early work on the density limit in tokamaks from the ORMAK [1] and DITE (2,3] groups has held up well over the years, results from recent experiments and the requirements for extrapolation to future experiments have prompted a new look at this

### Higher Plasma Densities, More Efficient Tokamaks

May 21, 2018 The density limit in tokamaks has been an experimental obstacle for decades. It s crucial to understand the density limit, because the fusion power produced by tokamaks is proportional to the square of plasma density; so the higher the plasma density the more power. This work correctly explains the density limit,

### A roadmap to the realization of fusion energy

High-density operation. In tokamaks, the edge plasma density cannot be increased above an empirical limit (the Greenwald density limit). The investigation of the origin of the limit and of possible ways to overcome it is an active field of research. One option being testedis the use of plasma density peaking to simultaneously respect the

### RECENT H-MODE DENSITY LIMIT EXPERIMENTS ON DIII-D

The MARFE condensation instability is a density dependent phenomenon which has been suspected to be the cause of the density limit in tokamaks. Figure 2 shows data from two discharges, one with 995 = 9, in which a MARFE occurred at a line density of 5 x 1019 corresponding to -0.8 nGW. The second discharge with 995 = 3.2 reached a line density of

### OPERATIONAL LIMITS AND LIMITING INSTABILITIES IN TOKAMAK MACHINES

The density limit is found to be a general observa-tion on all tokamaks and has been analyzed in detail by Greenwald [9]. In this paper he derived a very simple 0 500 1000 1500 2000 2500 125 175 225 −50 0 50 R / cm z / cm P rad / mW cm−3 Figure 2: Tomographic reconstruction of the radiated power density during a MARFE in the TEXTOR toka-mak.

### Density Limit Physics in

the density limit can be obtained. The steady state cooling rates, L(Z,T), for low density, high temperature plasmas in a corona model with the absence of transport effects can be rewritten as: Giannone L. et al., Density Limit Physics in Stellarators a) (3) I Time (s) Fig. 3 Overview of ECRH power ramp down discharges,

### A general comparison between tokamak and stellarator plasmas

In fusion plasmas, the maximum achievable density is limited basically due to the increase of impurity radiation with increasing density, which eventually leads to a collapse [16,17]. In tokamaks, the radiative collapse may cause a rapid cooling of the outer plasma boundary and a contraction of the

### The origins of tokamak density limit scalings

Stellarators are different than tokamaks Density limit clearly does not obey tokamak scalings Stellarator density limit is given by the Sudo limit M. Greenwald, et al., Plasma Phys. Control. A. Weller, et al., Nucl. Fusion 49 (2009) 065016 Fusion 44 (2002) R27 R80

### Transport Simulations of a Density Limit in Radiation

A density limit expressed in this form is often referred to as the Hugill limit. The Murakami limit is then the maximum density for all values of the plasma current. It is not clear how to extend the scaling law for the Hugill limit to include tokamaks having elongated cross sections due to the wide variety of analytic

### Plasma confinement properties at high density in TCV and T-10

the general regularity in th e density limit value on T-10. 2. The value of the density limit. Experiments on both tokamaks have been performed with gas puffing from the plasma periphery. The values of the limit density reached in T-10 and TCV are presented in Figure 1. Results of th e T-10 experiments with ohmic heating have

### The Physics Basis of ITER Confinement

The density is limited in tokamaks by the Greenwald limit (n e ≤ Ip/a 2) [5] and beta by the Troyon limit (β ≤ βNIp/aB) [6] all scale with current. Also the tokamak confinement time τE scales with plasma current (see equ. 1). Another important geometrical parameter in the design of tokamaks is triangularity.

### ID: 646 Stellaratorsas a Fast Path to Fusion

2. Scaling laws for stellaratorsand tokamaks are similar -both gyro-Bohm. Micro-turbulence can be optimized in stellarators. 3. Unfortunately, problems of axisymmetry (delicate stability, electron runaway, Greenwald density limit) not solved by simulation. 4. The W-7X island divertor, designed in 1996, is working as expected.

### Density limit of tokamaks - iopscience.iop.org

Apr 08, 2020 Density limit of tokamaks To cite this article: B. Lehnert 1983 Nucl. Fusion 23 1327 View the article online for updates and enhancements. Related content On particle transport in toroidal plasmas B Lehnert-Density limit of tokamak experiments B. Lehnert-The Quasi-steady Plasma-neutral Gas Balance in Magnetic Bottles B Lehnert-Recent citations

### Correlation of the Tokamak H-Mode Density Limit with

Operation of tokamaks with H-Mode [1] characteristics and at high densities is generally foreseen for future fusion power plants [2]. Here we show for JET and ASDEX Upgrade H-Mode plasmas, based on Thomson-scattering measurements, a clear correlation of the density limit of the tokamak H-Mode high-con nement regime with the approach to

### The Permanent Magnet Stellarator Simpler Stellarators for

Soft density and pressure limits Density limit much higher than tokamaks , easing divertor design Long divertor connection lengths, easing controlled detachment Sustained high βin LHD (4.8%) and W7-AS (3.2%). Ability to design for good confinement: W7X, HSX, LHD. Plasma Ion Temperature (keV) 10-1. 1. 10. 1. 10 2 58. 10

### MARTIN GREENWALD MIT - PLASMA SCIENCE & FUSION CENTER

density limit in tokamaks does not depend strongly on input power x x x x x x + + + + + 12 10 divertor ip = 0.5 1.9 ma bt = 0.8 2.1 t a ∼ 0.63 m b/a ∼ 1.8

### Princeton Plasma Physics Laboratory

the empirical density limit scaling for tokamaks known as the Greenwald limit [2, 3]. It has also been shown in Reference [4] that the current proﬁles corresponding to the density limit which were found in reference [1] generate small saturated islands at the q= 2 surface if only the classical ∆ ′ is used

### Higher plasma densities, more efficient tokamaks

The density limit in tokamaks has been an experimental obstacle for decades. It's crucial to understand the density limit. Why? Because in fusion power produced by tokamaks, the higher the

### Density limit in a ﬁrst principles model of a magnetized

empirical basis for tokamaks by Murakami [13], in the plasma physics com-munity the common opinion is rather that the density limit for tokamaks should be proportional to the Greenwald parameter I p/r2 a, where I p is the plasma current and r a the minor radius of the torus (see [1]).

### TRITA-PFU-84-08 DENSITY LIMITS IN TOKAMAKS M. Tendler

the density limit. Two additional explanations might be found assuming that the density limit is an edge phenomena and represents effectively the restriction on the maximum attainable edge density. The first possible reason might be the insufficiency of the power flow, arriving from the discharge interior to the recycling zone,to support losses

### Stellarator Operational Limits - Burning Plasma

limit observed in tokamaks. In W7AS, for example, the density limit was 0.5 0.5 nPVBe,max ≈1.5( / ) (MW, T, 10 20 m−3)[7], and densities 5 times the Greenwald limit were observed. The observations are in agreement with a theory explaining the limit in terms of a loss of power balance as the radiated power increases with density.

### Density limit of tokamak experiments Balance in Magnetic Bottles

Apr 18, 2020 Density limit of tokamaks B. Lehnert-Stability of plasmas penetrated by neutral gas B. Lehnert-Recent citations Density limits in toroidal plasmas Martin Greenwald-Density limit of tokamaks B. Lehnert-This content was downloaded from IP address 207.46.13.92 on 18/04/2020 at 01:27

### Explaining a mysterious barrier to fusion known as the

Explaining a mysterious barrier to fusion known as the 'density limit' 10 November 2015 Visualization of a magnetic island growing in a tokamak plasma.

### Request for 12000-18000 words

same empirical law. In tokamaks, where the most extensive studies have been conducted, there is strong evidence linking the limit to physics near the plasma boundary thus it is possible to extend the operational range for line-averaged density by operating with peaked density profiles. Additional particles in the plasma core

### Sudden loss of stored energy in tokamaks and stellarators

H-mode density limit in tokamaks M. Bernert et al. PPCF 57, 014038 (2015) Evolution of tokamak H-mode with density Constant gas puff from 1.5s W kin decreases P rad constant Full detachment of outer divertor (as for C density limit) immediately before disruption 5.8s MARFE at X-point moving upward tearing mode triggered

### 1 EX/P5-18 Tokamak Plasma Self-Organization and Possibility

tokamaks, τ eE, has different dependencies on the plasma density n e: for low densities (n e/n Gr<0.5) τ eE ∼ n e, but for higher densities (n e/n Gr>0.5) τ eE is practically independent from n e (fig. 2) Additionally, density fluctuation spectra measured by correlation reflectometry exhibit quite different spectra for low and high

### Multi-Machine Global Confinement and H-mode Threshold Analysis

Under some conditions with peaked density profiles, it is possible to achieve H factors IPB98(y,2) ~ 1 up to and beyond the Greenwald density limit and it is possible to achieve this level of energy confinement at a power level given by the H-mode threshold scaling (Eq. 1) evaluated at the full H-mode density.

### Hammett 2016 Unsolved Plasma Turbulence

* Tokamaks spontaneously spin: reduce turbulence & improve MHD stability. ITER spins more than previously expected? Up-down-asymmetric tokamaks/stellarators? * New stellarator designs, room for further optimization: Hidden symmetry discovered after 35+ years of fusion research. Fixes disruptions, steady-state, density limit.