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Курс лекций : Физико-технические основы токамака-реактора ИТЭР PowerPoint PPT Presentation


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Курс лекций : Физико-технические основы токамака-реактора ИТЭР. Владимир Юрьевич Сергеев проф., д.ф.м.н., кафедра физики плазмы физико-технический факультет СПбГПУ. Содержание лекции № 11-12 «Физика Scrape-off Layer ». 3.1. Взаимодействие плазмы с поверхностью 3.2. Scrape-off layer

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Курс лекций : Физико-технические основы токамака-реактора ИТЭР

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: - -

., ....,

-


11 12 scrape off layer

11-12 Scrape-off Layer

3.1.

3.2. Scrape-off layer

3.3. SOL

3.4.


3 scrape off layer

3 Scrape-off Layer

3.1.

3.2. Scrape-off layer

3.3.

3.4. SOL


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(plasma-wall interaction)

.

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- - . , .

, .

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- .

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(sheath)

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, . :

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.

.


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:

s . 6.5 (=0). s . - 0.8.


3 scrape off layer1

3 Scrape-off Layer

3.1.

3.2. Scrape-off layer

3.3.

3.4. SOL


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SOL

SOL . . . SOL ( )


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a ( LCFS), n - SOL ( e )

.


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n , V , - .

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, , n= L,


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,vn , e. , . ,

, .

p

-3


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Te(a) , , ( , , ). , , .

LCFS

SOL .

S p=n(Te+Ti) m .


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M = v/cs . , M 1 dM/dz . = 1 .

n(0) v = 0. , n(M)/n(0) 0.5 M 1.


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-0.69 Te/e M 1.

. .

. . .


3 scrape off layer2

3 Scrape-off Layer

3.1.

3.2. Scrape-off layer

3.3.

3.4. SOL


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LCFS. , . . , LCFS LCFS ( ). a2/ D. , .

LCFS. . .

. .


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. , . , . . , , . , , . , .

, . , , Rp , . RE


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Rp RE

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(reduced energy). :

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, 10 , , , .

, .

RE/Rp, 30-40% . 0.05 , . , , .

, , . . E0.


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, , . . . . ( ). .

, , . ( ) 100-500 .


3 scrape off layer3

3 Scrape-off Layer

3.1.

3.2. Scrape-off layer

3.3.

3.4. SOL


Semi analytical model for coupling core and edge plasma

Semi-Analytical Model for Coupling Core and Edge Plasma

Vladimir Sergeev1) and Boris Kuteev2)

e-mail: [email protected]

  • 1) State Polytechnical University, St. Petersburg, Russia

  • 2) Russian Research Centre Kurchatov Institute, Moscow, Russia

PET-12, Rostov Veliky , Russia, 02-04 September 2009


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Introduction

  • Integrated modelling of tokamak plasmas, which takes into account the effects of plasma control by heating, current drive, particle sources and plasma wall interaction, is of great importance for the contemporary tokamak program and for future reactor simulations. The integrated modeling is being developed in the framework of ITER/ITPA [1] and EFDA [2,3] activities joined by the attempts [4-6] to describe physical processes in specific fusion machines.

  • This work aims at a joint operation of most sophisticated codes, which separately describe MHD equilibrium and stability, transport, heating and current drives, fueling, SOL and divertor plasmas in tokamaks. This is a long-term strategic task for fusion plasma simulators. However, development of many tokamak subsystems, e.g. fueling and pumping, wall conditioning, heating and current drive, divertor etc., requires simpler approaches for simulations of coupled core and edge plasmas. The most important physical processes have to be taken into account in such a model. Simulations of this type were applied for analysis of fuelling in 0D [7] and for impurity injection in 1D approximations [8].

PET-12, Rostov Veliky , Russia, 02-04 September 2009


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Introduction (cont.)

  • In this article we consider a simple semi-analytical model which couples core and SOL regions of multi-species plasma that allows exploring steady state tokamak regimes with a broad range of plasma actuators.

  • Basic tokamak physics in a form acceptable for understanding the technology and operation basics should be established in such a model. Therefore, the most important control actuators, i.e. gas puffing and pumping, pellet and dust injection, auxiliary and fusion heating and recycling are incorporated in the model. This approach is helpful for analysis of tendencies of plasma behavior when impact of different actuators on a tokamak plasma is varied.

PET-12, Rostov Veliky , Russia, 02-04 September 2009


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Model basis

  • Two coupled core and SOL regions are responsible for heat, fuel and impurity flows in a tokamak. The interface of these regions is the plasma separatrix where solutions for different regions are matched. Consideration of the 2D tokamak core plasma region could be simplified to 1D approach. The SOL plasma is principally three-dimensional. Nevertheless, one should take into account at least 2D effects in this region. Processes of heat and particle transport should be also considered as coupled ones.

  • Basic physical processes (the radial diffusion/heat diffusivity, convection, sources and losses.) and the model assumptions in the core region are given in Table 1.

PET-12, Rostov Veliky , Russia, 02-04 September 2009


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Model basis (cont.)

PET-12, Rostov Veliky , Russia, 02-04 September 2009


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PET-12, Rostov Veliky , Russia, 02-04 September 2009

Model basis (cont.)


Layout of heat particle and radiation flows in a tokamak

PET-12, Rostov Veliky , Russia, 02-04 September 2009

Layout of heat, particle and radiation flows in a tokamak

A schematic diagram of lithium flows in a divertor tokamak with dust lithium jet injection in vicinity of the stagnation point is shown in Fig.1. Lithium is injected in small droplet form with the characteristic size of 20-30 microns and the velocity lower than 30 m/s [9-11]. The droplets are ablated in SOL [10] and the lithium ionized migrates to divertor plates that determines its density level in SOL. Interaction of lithium with peripheral plasma and with the wall during its transport along magnetic field lines from the injection point to the diverter determines the lithium density level in the SOL.

Fig.1


Essence of the analysis

PET-12, Rostov Veliky , Russia, 02-04 September 2009

Essence of the analysis

  • Four species were considered in the steady-state transport analysis: D, T, He and Li. The lithium film protection of the wall has allowed us to exclude heavy impurities from consideration. The density and temperature in the SOL were simulated by using the simple model of [12] taking into account different recycling coefficients RiRi for longitudinal (parallel) flows at the diverter plates for the species denoted by subscript i. The core density and temperaturewere calculated by using a set of transport equations assuming the anomalous diffusion D=0.3-0.6 m2/s, thermal diffusivity = (3-5)D and pinch velocity V = V(a)(r/a) to be equal for all species. Here, V(a) =0.075-0.6 m/s is the velocity magnitude at the separatrix, a is the separatrix radius and r is the minor radius. These assumptions correspond to the experiments and are close to those used in contemporary simulations (see [13]).

  • The source/loss location of species i is defined by radius r = bij, where j distinguishes the source/loss types when particles of species i appear in the plasma volume in different forms. For example, deuterium may be injected as a neutral gas or pellets and may be lost from the plasma in the form of ions due to fusion. The pumping rate for species i is equal to (1-Ri) part of the total corresponding flows into the SOL. The plasma heating sources produced by alpha particles, additional heating by the neutral beam injection and the electron cyclotron radiation were taken into account. Bremsstrahlung, as well as He and Li radiations in coronal approximation were considered similarly to [14], both in the core and SOL plasmas.


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PET-12, Rostov Veliky , Russia, 02-04 September 2009

Particle balance equations

For the core plasma region the following equation can be applied for

each ion specie i

Sij are delta-function particle sources for specie i located at radius bj,

fij(particles/sec) is the integral flow of i specie into the toroidal volume Vbj with radius bj.

Here, H is the Heaviside step function. The density profile can be calculated on the basis of the separatrix density ni(a).


Particle balance equations cont

PET-12, Rostov Veliky , Russia, 02-04 September 2009

Particle balance equations (cont.)

To evaluate the separatrix density ni(a) the plasma flow onto the divertor plate with sonic speed Vs of D-T mixture at average temperature Tav = 3 eV were assumed:


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Source position (Table 3)

PET-12, Rostov Veliky , Russia, 02-04 September 2009

  • MD+T is the average mass of the gas flow in the SOL, Ri is the recycling coefficient equal to 0.95 for gases (D, T, He) and equal to 0.1 for lithium, q95 is the safety factor at 95% flux surface. The SOL width SOL, or e-folding length, was assumed to be 2 cm in conformity with the range of values considered for ITER [15]. The separatrix density evaluated within these assumptions reasonably correlates with the empirical scaling presented in [12]. The set of particle and energy sources/losses included in the simulations with their normalized locations bij/a for all species are given in table 3.

*) The penetration depth of lithium dust at ITER conditions were evaluated on the basis of the Neutral Gas Shielding Model [16].


Heat balance equations

PET-12, Rostov Veliky , Russia, 02-04 September 2009

Heat balance equations

The heat transport was approximated by anomalous heat conductivity and particle heat transport in the core plasma. The electron and ion temperatures have been assumed equal each other Te=Ti =T.

This equation takes into account the particle transport described above and a homogeneous thermal diffusivity coefficient proportional to the diffusion coefficient D. The fusion heating source Q = 0.2Qfus, the neutral beam heating source QNBI and the ECRH source QECRH were approximated by -functions at the normalized minor radii bij/a=0.2, 0.3 and 0.6 respectively. The Ohmic heating term was neglected. Bremsstrahlung Qbr and mantle Qmtl radiation losses were placed at radii bij/a=0.2 and 0.9 correspondingly. Plasma dilution by cold pellet electrons was taken into account at bpell/a=0.8 as well. These radiation and pellet loss terms were taken into account iteratively (one-step approach).


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PET-12, Rostov Veliky , Russia, 02-04 September 2009

The temperature profile in the core plasma T(r)

For boundary conditions, we assumed the separatrix temperature Ts to be determined by the longitudinal electron heat transport [12]. The effect of the plasma radiation onto Ts was taken into account and the following equation

Here is the longitudinal heat conductivity coefficient [14], SSOL is the SOL cross-section area at the separatrix, Rc is the plasma major radius, Ibr and Imtl are the radiation power terms and P is the power of the corresponding heat source (fusion, NBI, ECRH). The temperature profile shape in the core plasma T(r) was calculated by using the following equation:


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Radiation model

PET-12, Rostov Veliky , Russia, 02-04 September 2009

Bremsstrahlung radiation in the core plasma was evaluated by using the density and temperature profiles, as well as the effective plasma charge profile Zeff[12]. This was calculated by the formula

(W/m3,m3,keV).

For the mantle Imtl and scrape-off layer ISOL radiations we used the model of [14]:

Here Li(T) is the emission rate coefficient of lithium or helium in coronal approximation [14]. T0 is the central plasma temperature. Both impurities are taken into account in the calculations of plasma radiation.


Basic goal of simulations with injected lithium

PET-12, Rostov Veliky , Russia, 02-04 September 2009

Basic goal of simulations with injected lithium

  • The basic goal of this study is searching for conditions when the major part of the fusion power is radiated by boundary plasma with injected lithium while the reactor core plasma remains low radiating and being clean enough with the effective charge below 1.7

  • The interest to the dust lithium jet technique is stimulated by necessity to provide wall conditioning in steady state operation and to reduce the total amount of lithium inside the vacuum vessel to a few kilogram level, which better corresponds to reactor safety requirements than the thick lithium wall with capillary porous system containing tons of lithium [17]


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PET-12, Rostov Veliky , Russia, 02-04 September 2009

The results of simulations

The results of calculating the plasma parameters in ITER&DEMO-like conditions for aV(a)/D=0.5 and 2 are given in Table 4 and Fig.2-4. Values of flows and power sources for different regimes are presented in Table 4. The lithium density profile is formed by the border source and looks most flat. The internal source at 0.5r/a for D and T produces a clear nipping effect on these profiles. The internal fusion source for He makes the corresponding profile mostly sharp. A strong effect of fusion reactions is seen in Fig.3 where the central densities of deuterium and tritium are obviously hollow in the case of aV(a)/D=0.5. Although that Zeffgrows towards plasma periphery due to lithium injection, the volume averaged value does not exceed the 1.6-1.7 acceptable level.

The temperature profiles (Fig.4a,b) give reasonable central values and demonstrate source location effects. Higher temperatures correspond to higher values of aV(a)/D.


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PET-12, Rostov Veliky , Russia, 02-04 September 2009

The results of simulations

Fig.2

Fig.3

Fig.4a

Fig.4b


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The results of simulations(Table 4)

PET-12, Rostov Veliky , Russia, 02-04 September 2009


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PET-12, Rostov Veliky , Russia, 02-04 September 2009

Discussion

  • The calculations show that lithium injection provides substantial increase of the radiation in the core and SOL plasma. Both for ITER&DEMO-like plasmas the Li and He radiations onto the divertor plates evaluated in coronal approximation reduce the heat flow onto divertor plates by a factor of 2.

  • However, the divertor heat loads are still high. From the thermal stability conditions of tokamak discharge it is possible to reduce the divertor heat loads upon to 0.2 of the total heat flow through separatrix [12].

  • To realize this condition it is necessary to enhance the impurity radiation by a factor of 2-5 as follows from the Table 4.


Summary

PET-12, Rostov Veliky , Russia, 02-04 September 2009

Summary

  • A simple semi-analytical model with coupled core and SOL regions with multi-species plasma that allows exploring steady state tokamak regimes has been developed. The most important control actuators, i.e. gas puffing and pumping, pellet and dust injection, auxiliary and fusion heating and recycling are incorporated into the model. Further improvement of the model presumes verification of its capability to describe experimental database of contemporary tokamak experiments with impurity injection.

  • In accordance with the analysis presented the lithium jet injection technique might have good perspectives for tokamak-reactor performance. For ITER and DEMO conditions the mantle and SOL might re-radiate more than a half of the total power with ~ 0.1 g/s lithium injection even in coronal approximation.

  • Stimulating the lithium recycling in the SOL volume by charge exchange and recombination processes may improve the situation significantly.

  • Although that Zeffgrows towards plasma periphery due to lithium injection, the volume averaged value does not exceed the 1.7 acceptable level under assumption of the 0.1 Li recycling coefficient. This assumption should be checked experimentally, which is planned in T-10 tokamak experiments.


References

PET-12, Rostov Veliky , Russia, 02-04 September 2009

References

[1] W.A. Houlberg, US Transport Task Force Meeting, 25-28 March 2008, Boulder, Colorado.

[2] A. Bcoulet et al., 21st IAEA Fusion Energy Conference, 16 - 21 October 2006, Chengdu, China, Topic TH/P2-22.

[3] V. Parail et al., 22nd IAEA Fusion Energy Conference, Geneva, Switzerland, October 13-18 2008, IT/P6-7.

[4] V. Parail et al., Plasma Physics Reports 29, 539544 (2003).

[5] H.R.Wilson et al., Nucl. Fusion 44, 917-929 (2004)

[6] D.P. Coster et al., Journal of Nuclear Materials 363365, 136139 (2007).

[7] H. Takenaga and the JT-60 Team. Development of fuelling system and its application to plasma control in JT-60U, ITER Fuelling Workshop, December 1 3 2008, Cadarache.

[8] B.V. Kuteev et al., 22nd IAEA Fusion Energy Conference, Geneva, Switzerland, October 13-18 2008, FT/P3-22.

[9] B.V. Kuteev et al., 21st IAEA Fusion Energy Conference, 16 - 21 October Chengdu, China, EX/P4-13 (2006)

[10] V.M. Timokhin et al.,33nd EPS Conference on Plasma Phys., Roma, 19 - 23 June 2006, Paper P-4.092

[11] V.M. Timokhin et al., 34th EPS Conference on Plasma Phys., Warsaw, July 2-6 2007, Paper P-1.205

[12] J.Wesson. Tokamaks, Clarendon Press, Oxford (2004)

[13] E.J. Doyle et al, Nucl. Fusion 47, S18 (2007)

[14] D. Post et al., Journal of Nuclear Materials 220-222, 1014 (1995)

[15] A. Loarte et al., Nucl. Fusion 47, S203 (2007)

[16] O.A. Bakhareva et al., Plasma Physics Reports 32,363 ( 2006)

[17] EVTIKHIN, V.A., et al., PPCF 44 (2002) 955-977.


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