Study of H- ion extraction and beam optics using the 2D3V and 3D3V PIC method

K. Miyamoto1), S. Nishioka2), S. Okuda3), I. Goto2), A. Hatayama2)

1) Naruto University of Education2) Faculty of Science and Technology, Keio University3) Toshiba corporation

Negative Ion Modeling Workshop, 16-18, September 2013, Keio University, Japan

Contents

1. Introduction

2. 2D3V PIC model (K. Miyamoto)1) Negative ion beam optics with integrated model (source plasma,

extraction region, and accelerator)・ Comparison of negative ion trajectories for beam core and beam

halo・ Emittance diagrams

2) The dependence of the plasma meniscus formation and beam halo on the physical parameters

3. 3D3V PIC model (S. Nishioka)・ Comparison of the plasma meniscus and beam halo fractions

between 2D and 3D models.

Introduction (I)

・ A negative ion source which can produce negative ion beams with high power and long pulse is the key component for the negative ion based NBI system for plasma heating and current drive of magnetic fusion reactors.

・ It is essential for the development of such a negative ion source to suppress heat loads of the acceleration grids and beamline components.

・ The heat loads of acceleration grids are mainly caused by the direct interception of H- ion beam as well as electrons stripped from negative ions in the accelerator.

・ Especially, a beam halo can result in the heat loads even at the optimum perveance for the beam core.

Beam halo component in the negative ion beam profile

Heat load on the acceleration grids due to the interception of negative ion beam

A1G

SL

D-

A2G GRG

Beam halo can be clearly observed on the log scale.

M.Kamada, M.Hanada, Y.Ikeda and L.R. Grisham, AIP Conf. Proc. 1097, 412 (2009).

H.P.L. de Esch, L. Svensson, Fusion Engineering and Design 86, 363 (2011)

The beam halo is observed directly as the beam profile, or indirectly as a component of the heat loads in the accelerator grids.

]

・ The purpose of our study is to clarify the physical mechanism of beam halo 　　 formation, especially the relation between the meniscus and beam halo, in order to suppress the heat load due to the direct interception of negative ion beams.

・ We have succeeded in the integrated modeling of negative ion beam from 　 plasma meniscus formation to the beam acceleration 　 by extending our previous 　　 2D3V PIC model .

・ Our extended model makes it possible to simulate not only the source plasma 　 with surface H- production, but also the H- acceleration self-consistently 　 without any assumption of plasma meniscus.

・ The dependence of the plasma meniscus formation and beam halo on the following physical parameters are investigated:

- Negative ion current density- Extraction voltage- Effective electron confinement time

Introduction (II)

2D PIC simulation model (I)

max~~ yy

min~~ yy

max~~ xx min

~~ xx

All the particles

PG

e

e

0~ 6350

~ H-

removed

EXG ESGA1G A2G GRG

e

+－

H+

electron

+

e

+

source plasma

× B-field for electron suppression

－－

－

Magnetic filter

Dirichlet condition

Physical quantities Symbol Normalization

Time

First 2D space coordinate

Second 2D space coordinate

Velocity

Electrostatic potential

Magnetic flux density

Current density

density

Cross field electron diffusion coefficient

tpet~

x~

y~

v~

Dex

Dey

thvv

~ ekTeB~

J~

n~

D~

emB pee

thevenj

PGyxe NNnN )(

peDeD 2

2D PIC simulation model (III)1. Main physical parameters in the source region

5.6×1010 rad/sElectron plasma frequency

7.4×10-6 mElectron Debye length

1018m-3Electron density

0.25 eV

0.25 eV (volume production)

1.4 eV (surface production)

Hydrogen ion temperature

1 eVElectron temperature

ValueSymbolPhysical parameters

eT

HT

HT

en

De

pe

・ Initial number of super-particles

electron: Ne = 9.5×105, H+: NH+ = 1×106, volume produced H-: NH- = 5×104

The ratio of NH- to Ne is determined from the experimental result of nH- / ne in the volume production.C. Courteille, A. M. Bruneteau, M. Bacal, Rev. Sci. Instrum., vol. 66, 2533-2540 (1995).

・ Electrons, H+ ions, and volume produced H- ions are assumed to be launched with Maxwellian distributions.

2D PIC simulation model (III)2. Electron Diffusion process across the transverse magnetic field due to electron-electron and electron-neutral collisions

//~~

2~xd tDx

A random-walk process with step lengths

21

1totepe

totee

e

m

kTD

normalized random number

e

Magnetic filter

e

//

3. Surface produced negative ions on the surface of the PG

EXGPG

H-

H-

H-

H-

H-H-

～x

～ y

・ Surface produced negative ions are uniformly launched from the PG surface with a half-Maxwellian distribution (TH- = 1.4 eV).

R. McAdams, A. J. T. Holmes, D. B. King, and E. Surrey,

Plasma Sources Sci. Technol. 20, 035023-1 (2011).

// A characteristic time of electron escape to the arc chamber

A characteristic time of electron diffusion across the magnetic filter

Simulation results of negative ion beam trajectory (I)

Snapshot of electrons and negative ions Negative ion beam profile near the exit of the GRG

PGEXG

ESG A1G A2G GRG

90

80

70

60

50

40

30

20

10

0

electron

～ y

～x

H- ion

0 200 400 600 800 1000 1200 1400 1600

～ J H-

y~

・ The present PIC code can reproduce the beam halo observed in an actual negative ion beam.

Simulation results of negative ion beam trajectory (II)

・ Negative ion current density

3 mA / cm2 (only volume production)

17.8 mA / cm2 (volume production + surface production)

・ Fraction of heat loads in the accelerator grids due to the intercepted negative ion beam are evaluated:

A1G: 0 %, A2G: 0.44 %, GRG: 3.2 %

　 The heat load due to the intercepted negative ions becomes larger in the downstream grid. This tendency agrees well with the experimental result.

Particle density profile around the PGH+ ion

H- ion

～ y

～x

908070605040302010 0

50 60 70 80 90 100 110 120 130

Hn~

～ y

～x

908070605040302010 0

50 60 70 80 90 100 110 120 130

Hn~

・ The surface produced H- ion density is high not only at the location of H- ion extraction aperture, but also in the bulk plasma away from the PG.

・ The electron density in the bulk plasma near the PG is negligible.

・ Therefore, the plasma quasi-neutrality is held by H+ and H- ion, i.e., double ion plasma. The present calculation result supports the experimental result.

K. Tsumori et al.,, Rev. Sci. Instrum., 83 02B116-1 (2012).

electron

～x

～ y

908070605040302010 0

50 60 70 80 90 100 110 120 130

en~

Potential Profile around the PG (I)Potential distributions

・ The potential well, which is formed in order 　　 to accelerate H+ ions and reflect the surface 　　 produced H- ions toward the PG.

- A. Hatayama, Rev. Sci. Instrum.79, 02B901/1-7 (2008); - F. Taccogna, P. Mineli, S. Longo, M. Captitelli, and R. Schneider,

Phys. Plasma, 17, 063502-1 (2010).

・ The depth of the potential well is evaluated to be approximately 0.5 eV.

Line (a)

Line (b)

～ y

～x

908070605040302010 0

50 60 70 80 90 100 110 120 130

Hn~

y~

～ φ

100~ x

～ φ

x~

40~ yLine(a)Line(b)

Potential Profile around the PG (II)～ y

～x

PG

～ y

～x

PG

Without surface produced negative ions

　 The electric field for the negative ion extraction is penetrated into the source plasma region along the PG surface.

With surface produced negative ions

Due to the space charge of these negative ions, the penetration of the electric field for the negative ion extraction is suppressed.

　 The potential profile with the surface produced negative ions is different from that without these negative ions:

Side wall

base

edge

Beam core trajectories

～x

～ y

PGEXG

ESG A1G A2G GRG

The surface produced negative ions move into the source plasma region, and are extracted from the central region of the meniscus.

These negative ions are focused by the electrostatic lens formed around the ESG.

～ y

PGEXG

～x

90

80

70

60

50

40

30

20

10

0　 0 200 400 600 800 1000 1200 1400 1600

Beam halo trajectories

90

80

70

60

50

40

30

20

10

0　 0 200 400 600 800 1000 1200 1400 1600

～x

PGEXG

ESG A1G A2G GRG

The surface produced negative ions, which are launched from the side wall or the edge of the PG aperture, are over-focused due to the curvature of the edge of the meniscus.

Since the electrostatic lens near the beam axis hardly focuses the negative ion beams, these negative ions have large divergent angles, and become the beam halo.

～ y

PGEXG

～x

～ y

Emittance diagrams

10 20 30 40 50 60 70 80 90

10

5

0

-5

-10

-1510 20 30 40 50 60 70 80 90

1

0.5

0

-0.5

-1

10 20 30 40 50 60 70 80 90

0.15

0.1

0.05

0

-0.05

-0.1

-0.15

～ y

～x

90

80

70

60

50

40

30

20

10

060 80 100 120 140 160 180 200 220 240

～y

Div

erge

nce

angl

e (r

ad)

～y

Div

erge

nce

angl

e (r

ad)

～y

Div

erge

nce

angl

e (r

ad)

Line (a) Line (b)

Line (c)

PG EXG ESG Beam core Beam halo

Summary We have developed the integrated 2D PIC code for the analysis of the physics of the beam halo formation, which can simulate not only the source plasma with surface H- production, but also the H- acceleration self-consistently without any assumption of plasma meniscus.

・ The simulation code reproduces a beam halo observed in an actual negative ion beams.

・ The following physical mechanism of halo formation is shown:

The negative ions extracted from the periphery of the meniscus are over-focused in the extractor due to large curvature of the meniscus. Theses ions are not focused by the electrostatic lenses in the accelerator, and consequently result in the beam halo.

　

Future PlaneThe following optimization of the PIC model will be planed:

・ Global 3D PIC model with the parallelization: more precise modeling electron loss along/across the field line, because the plasma meniscus strongly depends on it.・ Coupling of the PIC code with a Monte Carlo code (PIC-MCC)- surface production process via H atoms and H+ ions- H- destruction process, for example, mutual neutralization

The dependence of the plasma meniscus formation and beam halo on the physical parameters

Simulation model

H- Ion Source 　　　　　　　　 Extraction region

Number of meshes　 X = 170, Y = 94Size of meshes　 DX=DY=0.5Length of time step　 1 Time Step = t / 10Number of particles　 H+: 1.0×105

　 H‐: 1.0×104

　　 e: 9.0×104

~

I. Effect of negative ion current density on plasma meniscus

3 H- surface production / time step 15 H- surface production / time step

y~

x~x

~

The penetration of the plasma meniscus is small under a large amount of H- surface production.

(a) (b)

Comparison of 2D profiles of H- ion density

II. Effect of extraction voltage on plasma meniscus

Normalized EG potential: 120 Normalized EG potential: 180

y~

x~x

~

Comparison of 2D profiles of H- ion density

As the extraction voltage is larger, the penetration of the plasma meniscus becomes larger as and consequently the fraction of the beam halo increases .

(a) (b)

III. Effect of electron confinement on plasma meniscus From the comparison without and with the magnetic filter, it is

suggested that the fraction of beam halo depends on the electron density near the PG aperture.

The electron density depends on the effective electron confinement time in the source plasma.

In the present simulation, the effective electron confinement time can be varied by changing the parameter of .

The large value of means that the effective electron confinement time is long, and thus, the electron density near the PG aperture becomes high.

//

//

Comparison of 2D density profiles

01.0// electron density 04.0//

negative ion density

01.0// 04.0//

In the case of the short effective electron confinement time, the penetration of the plasma meniscus into the source plasma becomes deep since the Debye shielding of the H- extraction electric field becomes small. Thus, the fraction of the beam halo increases.

The electron confinement time depends on the characteristic time of electron escape along the magnetic field as well as the characteristic time of electron diffusion across the magnetic field. Therefore, it is indicated that such parameters as the strength of the magnetic filter and the size of the arc chamber are important for the design of the negative ion sources to reduce the beam halo.

2D PIC simulation model (IV)

Electric field Magnetic field

5.1

2

5.1

2

realext

HrealPG

simext

HsimPG

V

Jr

V

Jr

(1) Extraction voltage

The extraction voltage is modeled in order to match the perveance for the real negative ion source.

(2) Acceleration voltages

The applied voltages in the accelerator are modeled to satisfy the law of scaling.

realrealrealsimsimsim VVVVVV 321321 ::::

V1 : voltage in the first gap (ESG-A1G)

V2 : voltage in the second gap (A1G-A2G)

V3 : voltage in the third gap (A2G-GRG)

・ The scale is normalized by the electron Debye length. Since this large different size between the electron Debye length and the real negative ion source will cause considerable high computation cost, the simulation model is scaled down.

Lsim = s Lreal (s :scale factor)

・ The strengths of the applied voltages and the magnetic field are modeled followed by the scale down:

.3/1realsim BsB

The magnetic field in the simulation is given by the scale down of the Larmor radii of electrons:

.realreal

simsim B

sv

vB

realextsimext VsV 3/4

.3/2sV

V

v

v

real

sim

real

sim

Beam optics study JAEA

Culham

Linear scale

Log scale

Linear scale

A. J. T. Holmes and M. P. S. Nightingale, Rev. Sci. Instrum., 57, 2402 (1986).

K. Miyamoto et al., in Proceeding of the joint meeting of the 7th International Symposium on the Production and Neutralization of Negative Ions and Beams and 6th European Workshop on the Production and Application of Light Negative Ions (Upton, New York, Oct. 23 ~ 27, 1995), AIP CONFERENCE PROCEEDINGS 380 (1996) pp. 390 ~ 396.

Log scale