design of the mitica neutral beam injector: from physics

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1 ITR/1-3 Design of the MITICA neutral beam injector: from physics analysis to engineering design P. Sonato a , D. Boilson b , T. Bonicelli c , A.K. Chakraborty d , C. Day e , P. Franzen f , G. Gorini g , T. Inoue h , J. Milnes j , T. Minea k , H.P.L. De Esch l , P. Agostinetti a , M. Agostini a , V. Antoni a , M. Barbisan a , P. Bettini a , M. Bigi a , M. Boldrin a , M. Brombin a , M. Cavenago m , G. Chitarin a , G. Croci n , M. Dalla Palma a , S. Dal Bello a , M. De Muri a , A. De Lorenzi a , F. Fellin a , A. Ferro a , A. Fiorentin a , L. Grando a , S. Hanke e , M. Kashiwagi h , A. Luchetta a , G. Manduchi a , N. Marconato a , D. Marcuzzi a , R. Pasqualotto a , M. Pavei a , S. Peruzzo a , A. Pesce a , N. Pilan a , N. Pomaro a , M. Recchia a , W. Rigato a , A. Rizzolo a , E. Sartori a , G. Serianni a , A. Soppelsa a , A. Sottocornola a , M. Spolaore a , C. Taliercio a , M. Taniguchi h , H. Tobari h , V. Toigo a , M. Valente a , P. Veltri a , K. Watanabe h , P.Zaccaria a , B. Zaniol a , A. Zamengo a , L. Zanotto a a Consorzio RFX, Euratom-ENEA association, Padova, Italy b Iter Organization, St Paul Lez Durance, France c Fusion for Energy, 08019 Barcelona, Spain d Iter India, Gandhinagar, India e Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany f Max-Planck-InstitutfürPlasmaphysik, Garching b. Muenchen, Germany g Università degli Studi di Milano-Bicocca, Milano, Italy h JAEA, Naka Fusion Institute, Naka-shi, Ibaraki, Japan j Culham Centre for Fusion Energy, Abingdon, Oxfordshire, United Kingdom k Université de Paris Sud – Orsay Cedex, Paris, France l CEA, IRFM, F-13108, Saint-Paul-Lez-Durance, France m INFN-LNL, Legnaro, Italy n IFP-CNR, Milano, Italy E-mail contact of main author: [email protected] Abstract. For ITER heating and current drive, two neutral beam injectors (NBIs) are planned, delivering a total of 33 MW in stationary conditions up to one hour; each injector will accelerate a 40 A D - current up to 1 MV. Such requirements have never been achieved simultaneously. Hence the PRIMA (Padova Research on ITER Megavolt Accelerator) facility is under construction at Consorzio RFX in Padua, Italy. PRIMA will include a test bed named MITICA, with the aim of reliably meeting the ITER heating beam requirements. This contribution describes the current status of analysis, devoted to the optimization of MITICA, providing the inputs for the design of accelerator, beam line components, diagnostics, power supplies, control-data acquisition and interlock systems. 1. Introduction The operation of the ITER thermonuclear fusion experiment will require a mix of heating systems with the aim of supplying the plasma with additional power to demonstrate the sustainability of the fusion reactions with a Q factor ranging from 5 to 10 in a stationary condition [1]. Among the heating systems, two neutral beam injectors (NBIs), are planned, delivering a total of 33 MW up to one hour; each injector will accelerate a 40 A D - ion current up to 1 MV. Such requirements have never been achieved simultaneously. To minimise risks and time to provide ITER with reliable NBIs, the ITER Organization and the parties involved in the development of the NBIs (EU, Japan and India) have endorsed the construction of a test facility for the experimental optimisation of critical components and systems. The PRIMA (Padova Research on ITER Megavolt Accelerator) facility at Consorzio RFX in Padua (Italy) will test the ITER injector prototype MITICA (Megavolt ITer Injector and Concept Advancement) (FIG. 1). MITICA will have the following aims: achieve the specified negative ion yield and caesium consumption; study the beam uniformity and high voltage

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Page 1: Design of the MITICA neutral beam injector: from physics

1 ITR/1-3

Design of the MITICA neutral beam injector: from physics analysis to

engineering design

P. Sonatoa, D. Boilson

b, T. Bonicelli

c, A.K. Chakraborty

d, C. Day

e, P. Franzen

f, G. Gorini

g, T.

Inoueh, J. Milnes

j, T. Minea

k, H.P.L. De Esch

l, P. Agostinetti

a, M. Agostini

a, V. Antoni

a, M.

Barbisana, P. Bettini

a, M. Bigi

a, M. Boldrin

a, M. Brombin

a, M. Cavenago

m, G. Chitarin

a, G.

Crocin, M. Dalla Palma

a, S. Dal Bello

a, M. De Muri

a, A. De Lorenzi

a, F. Fellin

a, A. Ferro

a, A.

Fiorentina, L. Grando

a, S. Hanke

e, M. Kashiwagi

h, A. Luchetta

a, G. Manduchi

a, N.

Marconatoa, D. Marcuzzi

a, R. Pasqualotto

a, M. Pavei

a, S. Peruzzo

a, A. Pesce

a, N. Pilan

a, N.

Pomaroa, M. Recchia

a, W. Rigato

a, A. Rizzolo

a, E. Sartori

a, G. Serianni

a, A. Soppelsa

a, A.

Sottocornolaa, M. Spolaore

a, C. Taliercio

a, M. Taniguchi

h, H. Tobari

h, V. Toigo

a, M. Valente

a,

P. Veltria, K. Watanabe

h, P.Zaccaria

a, B. Zaniol

a, A. Zamengo

a, L. Zanotto

a

aConsorzio RFX, Euratom-ENEA association, Padova, Italy

bIter Organization, St Paul Lez Durance, France

c Fusion for Energy, 08019 Barcelona, Spain

dIter India, Gandhinagar, India

e Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany

fMax-Planck-InstitutfürPlasmaphysik, Garching b. Muenchen, Germany

gUniversità degli Studi di Milano-Bicocca, Milano, Italy

hJAEA, Naka Fusion Institute, Naka-shi, Ibaraki, Japan

jCulham Centre for Fusion Energy, Abingdon, Oxfordshire, United Kingdom

kUniversité de Paris Sud – Orsay Cedex, Paris, France

lCEA, IRFM, F-13108, Saint-Paul-Lez-Durance, France

mINFN-LNL, Legnaro, Italy

nIFP-CNR, Milano, Italy

E-mail contact of main author: [email protected]

Abstract. For ITER heating and current drive, two neutral beam injectors (NBIs) are planned, delivering a total

of 33 MW in stationary conditions up to one hour; each injector will accelerate a 40 A D- current up to 1 MV.

Such requirements have never been achieved simultaneously. Hence the PRIMA (Padova Research on ITER

Megavolt Accelerator) facility is under construction at Consorzio RFX in Padua, Italy. PRIMA will include a test

bed named MITICA, with the aim of reliably meeting the ITER heating beam requirements. This contribution

describes the current status of analysis, devoted to the optimization of MITICA, providing the inputs for the

design of accelerator, beam line components, diagnostics, power supplies, control-data acquisition and interlock

systems.

1. Introduction

The operation of the ITER thermonuclear fusion experiment will require a mix of heating

systems with the aim of supplying the plasma with additional power to demonstrate the

sustainability of the fusion reactions with a Q factor ranging from 5 to 10 in a stationary

condition [1]. Among the heating systems, two neutral beam injectors (NBIs), are planned,

delivering a total of 33 MW up to one hour; each injector will accelerate a 40 A D- ion current

up to 1 MV. Such requirements have never been achieved simultaneously. To minimise risks

and time to provide ITER with reliable NBIs, the ITER Organization and the parties involved

in the development of the NBIs (EU, Japan and India) have endorsed the construction of a test

facility for the experimental optimisation of critical components and systems.

The PRIMA (Padova Research on ITER Megavolt Accelerator) facility at Consorzio RFX in

Padua (Italy) will test the ITER injector prototype MITICA (Megavolt ITer Injector and

Concept Advancement) (FIG. 1). MITICA will have the following aims: achieve the specified

negative ion yield and caesium consumption; study the beam uniformity and high voltage

Page 2: Design of the MITICA neutral beam injector: from physics

2 ITR/1-3

holding; investigate beam particle trajectories in

the accelerator and the neutralization process; test

beam line components at full power; prove correct

operation of the residual ion dump; fully testing

the power supplies; verifying the overall reliability

of the NBI.

The present contribution describes the current

status of MITICA, highlighting the simulation

effort made at Consorzio RFX in collaboration

with the other international partners.

2. Negative ion production

Negative ions for neutral beam injectors are

generated in a RF-driven D (or H) plasma source

along two different processes: surface production

and volume production. In the latter case, ions are

due to dissociative attachment of low energy electrons to rovibrationally excited molecules; in

the former one, the deposition of caesium on the surfaces reduces their work function, thus

increasing the secondary emission of negative ions from the surface of the first electrode,

called Plasma Grid (PG) when bombarded by plasma particles [2]. After being directed

towards the PG apertures, negative ions encounter the meniscus, a thin region playing the role

of plasma boundary and regulating the amount of extracted particles. Ion transport codes are

used to optimise the geometry of the upstream side of the plasma grid in order to maximize

the extraction of negative ions in the presence of electrostatic and magnetic fields [3]. Several

different models are used (e.g. [4], [5], [6]) to study the extraction region.

3. Negative ion acceleration and accelerator design

The starting point for the accelerator design was the ITER Multiple-Aperture Multiple-Gap

(MAMuG) concept [7], but the present design results from a collaborative work based on

experimental results and computations proposed by several international partners [8].

The main technical requirements of the MITICA experiment are as follows [9]:

- for deuterium operation: beam energy 1000keV; accelerated current 40A;

- for hydrogen operation: beam energy 870keV; accelerated current 49A;

- beamlet divergence ≤7 mrad; beam-on time 3600 s.

The plasma source and the PG are kept at about -1 MV with respect to ground potential. The

negative ions are initially drawn through the EG (a voltage of about 10 kV is applied between

the PG and the EG) and then through five acceleration grids (AGs). Voltages of 200 kV are

applied between adjacent grids, the last grid being at ground potential (FIG: 2). Undesired

electrons, extracted from the ion source together with the negative ions, are dumped onto the

EG by means of a magnetic field generated by permanent magnets embedded in the EG itsel

In addition to the codes already used for the design of the 100 kV prototype accelerator

SPIDER [10], a number of new numerical codes and pre- and post-processing tools have been

developed for the design of MITICA in order to better describe the most prominent

phenomena in the accelerator physics.The codes used are the following: SLACCAD for self-

consistent electrostatic cylindrically symmetrical simulations and beam optics assessment,

including stripping [11]; AVOCADO, based on the viewing factor technique [12], for density

profile reconstruction; OPERA for multi-beamlet 3D optics analyses, including stripping [13];

NBImag for the evaluation of magnetic fields generated by arbitrary configurations of currents

and permanent magnets [14]; EAMCC for particle tracking in 3D electrostatic and magnetic

fields, including the generated

FIG. 1: View of MITICA injector

15 m

Page 3: Design of the MITICA neutral beam injector: from physics

3 ITR/1-3

secondary particles, providing the estimation of heat

loads on the grids, transmitted beam and amount of

back-streaming positive ions [15][16] (FIG.3);

ANSYS for thermo-mechanical and magnetic

analyses[17]. In such an endeavour as the design of

the MITICA accelerator, validation of the codes

against experimental data is necessary and is in

progress with respect to data collected at NIFS [18]

and at IPP [19].

Several different geometries and magnetic

configurations have been considered for the

downstream side of the PG, the Extraction Grid (EG),

which give advantageous effect on the extracted ion

current, and for the accelerator. The various proposals have been compared in terms of: beam

optics (beamlet divergence, beam aiming); amount of co-extracted and stripped electrons to be

dumped; thermo-mechanical loads on accelerator grids and beam line components; voltage

holding capability. The effect of beam halo and possible variations of the operating scenario

have also been studied. It was found that a horizontal “long range” field of about 1 mT in the

accelerator, combined with a “local” vertical field, produced by permanent magnets embedded

in the AGs, appears to be the most effective solution in limiting both the electrons transmitted

out of the accelerator and the maximum load on the grids. The configuration of the accelerator

that is presently considered along the optimization process is shown in FIG. 2 [20]. The "long

range" field in the accelerator is produced by currents flowing in the plasma grid and in

dedicated busbars according

to the arrangement shown in

FIG. 3. Such magnetic

configuration has been

optimized also in terms of

spatial uniformity both

inside and outside the

accelerator using a

"simulated annealing"

optimization procedure

[21].This solution will be

adopted both in MITICA

FIG. 2: Section view of MITICA accelerator geometry; the grid cooling channels and the embedded

magnets are also shown (bulk material is Cu-Cr-Zr, blue areas show the cooling channels and the

arrow areas show the permanent magnets with their magnetic flux direction).

FIG.3: Example of core particle

transmission. BLUE lines are D- and

RED lines are electron trajectories

FIG. 4: Layout of busbars (orange bars) in the beam source and

magnetic field profile in different points of the extraction area

Page 4: Design of the MITICA neutral beam injector: from physics

4 ITR/1-3

and ITER Heating Neutral Beam; in

MITICA larger flexibility is added thanks to

coils located on the outer side of the vacuum

vessel, which allow to optimize the field

strength in the plasma source and accelerator

regions during the experimental campaign.

The expected pressure profile inside the

MITICA accelerator is computed including

the detailed geometry of the accelerator; the

result is displayed in FIG. 5 [22].

The heat deposited on the accelerator grids

induce stresses and deformations (in-plane and out of plane) which are estimated by means of

thermo-mechanical analyses as shown in FIG. 6.

These computations are carried out by including the simulation of the active cooling by means

of dedicated non-linear analytical models [23]. The trajectories of electrons exiting the

accelerator are computed including their probability of being backscattered at the various

surfaces FIG. 7. Thus powers and power densities deposited on the beam line components are

estimated [24] and suitable devices (electron dump; baffles) are realised to cope with the heat

loads. Outside the accelerator the negative ions interact with the background gas; ionization

ensues so that the beam space charge can be compensated by positive charges. Simulations to

assess this phenomenon are

performed to estimate the final

divergence of the beam and

consequently the amount of

interaction between the beam and the

beam line components[25]. The

results of thermo-mechanical

analyses are post-processed by

applying the ASME and the

Structural Design Criteria for ITER

in-vessel components.

FIG. 5: Estimated gas density profiles along the

accelerator and in different beamlet position.

FIG. 6: In-plane (left) and out-of-plane (right) deformations of relevant accelerator grids

FIG. 7: Trajectories of electrons exiting the accelerator

and backscattered at the surfaces of vessel and power

load density on the vessel surface (kW/m2)

Page 5: Design of the MITICA neutral beam injector: from physics

5 ITR/1-3

The breakdown of stresses is accomplished

according to the norm, and all necessary

verifications are carried out (static,

ratcheting, fatigue). Moreover, grid

deformations are verified against possible

influence on beam optics: out-of-plane

deformations must be minimized for each

grid, to maintain the beamlet optics, in-

plane deformations must be managed on

the whole set of grids, in order to limit

misalignments of different grids [10].

Detailed structural Finite Element (FE)

analyses are necessary for several sub-

systems of the MITICA Beam Source. For example verifications are carried out in order to

verify the structure supporting the copper accelerator grids: first, a global static analysis gives

an overview of the system behaviour (as shown in FIG. 8), then further evaluation studies are

performed on specific issues. Dedicated analyses, based on a statistical method suitable for

fragile materials, are carried out in order to verify the ceramic

insulators.

The seismic verifications are a relevant point within the load

case specification. An official IO document gives the

guidelines to tackle this issue: response spectra indicate that

having a structure with eigen-frequencies higher than 15-20

Hz is always a recommended approach, hence quick and

useful indications are given by modal analysis (FIG. 9).

4. HV holding of beam source: models and criteria

2D electrostatic analyses on vertical and horizontal symmetry

planes have been carried out for preliminary assessment of

HV holding and benchmarked with full 3D FE models.

However, once the electrostatic field maps are available, the

sole electric field strength cannot be directly adopted to

optimize a multi-electrode multi-voltage system insulated by

large vacuum gaps; the experimental results, typically carried

out using simply plane parallel electrodes, highlights the

correlation E.α

.d

-0.5 between E (electric field) and the gap

length d.

Moreover,

generally

speaking, the voltage holding performances

are characterized by a spread of experimental

results depending on materials, surface

finishing, cleanliness, conditioning

procedures and dimensions of facing areas.

A new design criterion has been therefore

developed [26]: it is based on the

implementation of the micro particle (clump)

induced breakdown Cranberg-Slivkov theory

FIG. 8: Global static analysis of the grids support

structure of the beam source

FIG. 9: Modal analysis of the

grids support structure

Micro-particles (clumps)

trajectories

0 0.5 1 1.5 2 [m]

[V]

Max: 0 V

Min: -10e05 V

0 V

-1.0 MV

0 V

Equipotential

Lines distribution

Micro-particles (clumps)

trajectories

0 0.5 1 1.5 2 [m]0 0.5 1 1.5 2 [m]

[V]

Max: 0 V

Min: -10e05 V

0 V

-1.0 MV

0 V

Equipotential

Lines distribution

FIG. 10: Electrostatic field map and breakdown

probabilistic analyses on beam source

horizontal cross section

Page 6: Design of the MITICA neutral beam injector: from physics

6 ITR/1-3

into a statistical approach defined by

the Weibull’s two parameters

distribution. The results of

electrostatic analyses and breakdown

probability

estimation, considering the micro-

particles trajectories (FIG. 10),

allows to identify the critical points

for high voltage holding, then

reducing step by step, the breakdown

probability of the system.

In parallel to numerical simulations, a

new High Voltage Test Facility [27] has been built and commissioned to support the design

and R&D activities related to the MITICA electrostatic accelerator.

5. Beam line components

Three beam line components are foreseen in

MITICA: the Neutraliser and Electron Dump

(NED), the Electrostatic Residual Ion Dump

(ERID) and the calorimeter.

Beams of energetic atoms are produced

inside the neutraliser by charge-exchange

collisions between the 1 MeV D-(H

-) ion

beam exiting the beam source and D2 (H2)

gas molecules. This neutralization process

occurs inside four beam channels separated

by five actively cooled Cu plates. This

geometry gets an optimum neutralisation efficiency with limited gas injection in the order of

19 Pa.m

3/s for D2 (43 for H2), required to keep acceptable pressure inside the injector and

limit the regeneration requirements for the cryogenic pump. Details of NED panels and

leading edge elements are shown in FIG. 11. A total flow rate of 50 kg/s is shared among the

leading edge elements, the panels and the electron dump. Further actively cooled Cu plates

located on the beam entrance side of the neutraliser form the electron dump, designed to dump

the post accelerated electrons escaping from the beam source, so shielding the side cryopumps

and the vessel walls.

The four beam channels structure separated by five actively cooled panels is then replicated

for the ERID, where the residual positive and negative ions exiting the NED are deflected by a

20 kV transverse electrostatic field applied between alternate panels. Each of the five ERID

panels is composed of 18 CuCrZr elements (see FIG.12). Cooling channels with swirled SS

tapes are foreseen to enhance

thermal exchanges between water

and panels bulk material.

A calorimeter is necessary to dump

the entire beam and used to

characterize the beam properties.

The two panels forming the “V

shaped” calorimeter are shown in

FIG. 13. Each of the panels is

composed of a stack of 96 CuCrZr

Beam

NED

assemblyCooling

pipework with

actively cooled

elements

Leading

Edge

Elements

FIG. 11: NED and details of the panel and leading edges

ERID

assembly

Panel : cooling

pipework with

actively cooled

elements

FIG. 12: ERID and detail of one panel

Calorimeter

assemblyPanel : cooling

pipework with

actively cooled elements

BEAM

5.5°6.2°

BEAM

5.5°6.2°

FIG. 13: Calorimeter assembly and upper view

Page 7: Design of the MITICA neutral beam injector: from physics

7 ITR/1-3

tubes with SS swirled tape inside.

An intermediate support element

is foreseen to reduce the

maximum free length of the tubes,

aiming to limit the excessive

horizontal deformations and

vibrations calculated for the

original design having 2 m long

cooling tubes.

The main gas sources in the

injector are the Neutraliser and the

plasma source, this last source of

gas is approximately the 20% of the gas required by the Neutraliser; other minor relevant

sources of gas are all the surface hit by the beam particles. The conflicting requirements on the

gas flow and on the vacuum level impose to design very large cryogenic pumps operating at

4.5 K to adsorb the D2 (or H2) on surfaces coated with charcoals. The cryogenic panels are

shielded by screens at approximately 80 K. They are installed in the vessel along the whole

length of the two lateral walls as shown in FIG. 14 for an overall length of approximately 8 m

for each pump. The cryogenic pump is designed as an open structure to maximize the

pumping speed: each 4.5 K pumping stage is individually shielded on the vacuum side,

whereas a full closed shield is foreseen on the vessel wall side.

The design of the cryogenic pumps has required thermo-mechanical analyses considering

several operational scenarios with temperatures ranging from the liquid helium temperature up

to the room temperature [28]. The heat loads on cryopumps have been considered, arising

from radiation exchanges and from beam particles hitting the cryogenic walls at very wide

energy spread (from thermal to high

energy particles). Functional

verifications required further

analyses to assess the particle

throughput in the different zone of

the very long cryogenic pump. A

3D model, shown in FIG. 15 has

been developed and used to study

the pressure profile in the

Neutraliser and the gas flow to the

cryogenic pumps inside the vessel,

using a Monte Carlo [29] and the

AVOCADO code[12].

6. Conclusion

The paper presents the development of the design of MITICA, the prototype heating neutral

beam injector for ITER, starting from physic requirements, necessary to guarantee the

performances required for ITER to fulfil the expected the fusion power gain, up to the

development of the engineering requirements by using a number of original and commercial

numerical analysis codes.

An integrated design approach is necessary and involves all the design stages of all the

components and plant systems. The progress of the design foresees a continuous cyclic check

of the requirement consistency towards a robust design fulfilling all physics needs and

constraints and all engineering practices in all the technology fields.

FIG. 14: Cryogenic pumps and detail of the three cryopanel

stages (upper side is the vessel wall side)

FIG. 15: gas pressure in the Neutraliser and gas

throughput on the cryogenic pumps

Page 8: Design of the MITICA neutral beam injector: from physics

8 ITR/1-3

In 2012 the design is converging towards the completion of the main design activities of all

the main items and main plant systems of MITICA.

Acknowledgements and disclaimer

The views and opinions expressed herein do not necessarily reflect those of the ITER

Organization.

This work was set up in collaboration and financial support of F4E.

References [1] WAGNER, F., et al., “On the heating mix of ITER”, Plasma Phys. Control. Fusion 52 (2010) 124044.

[2] BACAL, M., “Physics aspects of negative ion sources”, Nucl. Fusion 46 (2006) S250.

[3] GUTSER, R. et al., “Negative hydrogen ion transport in RF-driven ion sources for ITER NBI”, Plasma Phys.

Control. Fusion 51 (2009) 045005

[4] CAVENAGO, M., et al., “Negative Ion Extraction With Finite Element Solvers and Ray Maps”, IEEE Trans.

Plasma Sci. 36 (2008) 1581.

[5] TACCOGNA, F., et al., “Modelling of a negative ion source. III. Two-dimensional structure of the extraction

region”, Phys. Plasmas 17 (2010) 063502.

[6] LISHEV, ST., et al., “Analysis of the factors determining the extraction of negative ion beams from plasma

sources”, Nucl. Fusion 51 (2011) 043008.

[7] INOUE, T., et al., “Design of neutral beam system for ITER-FEAT”, Fusion Eng. Des. 56-57 (2001) 517.

[8] DE ESCH, H.P.L., et al., “Physics design of the HNB accelerator for ITER”, 3rd Int. Symp. on Negative Ions,

Beams and Sources, 2012, Finland; submitted to AIP Conf. Proc.

[9] HEMSWORTH, R., et al., “Status of the ITER heating neutral beam system”, Nucl. Fusion 49 (2009) 045006.

[10] AGOSTINETTI, P., et al., “Physics and engineering design of the accelerator and electron dump for SPIDER”,

Nuclear Fusion 51 (2011) 063004.

[11] DE ESCH, H.P.L., et al., “Updated physics design ITER-SINGAP accelerator”, Fusion Eng. Des. 73 (2005) 329.

[12] SARTORI, E. et al., “AVOCADO: a numerical code to calculate gas pressure distribution”, submitted to Vacuum.

[13] OPERA-3D, Vector Fields Co.Ltd., http://www.vectorfields.com/.

[14] CHITARIN, G., et al., “An integral formulation for eddy current analyses in axisymmetric configurations”, IEEE

Trans. Magnetics, 25 (1989) 4330.

[15] FUBIANI, G., et al., “Modeling of secondary emission processes in the negative ion based electrostatic accelerator

of the International Thermonuclear Experimental Reactor”, Phys. Rev. Special Topics Accel. Beams 11 (2008)

014202.

[16] FUBIANI, G., et al., “Analysis of the two accelerator concepts foreseen for the neutral beam injector of the

International Thermonuclear Experimental Reactor”, Phys. Rev. Special Topics Accel. Beams 12 (2009) 050102.

[17] ANSYS Manual, ANSYS Inc., http://www.ansys.com/

[18] AGOSTINETTI, P., et al., “Modeling activities on the negative-ion-based Neutral Beam Injectors of the Large

Helical Device”, AIP Conf, Proc. 1390 (2011) 526

[19] AGOSTINETTI, P., et al., “Benchmark of the SLACCAD code against data from the MANITU testbed at IPP”, 3rd

Int. Symp. on Negative Ions, Beams and Sources, 2012, Finland; submitted to AIP Conf. Proc.

[20] AGOSTINETTI, P., et al., “Optimization of the electrostatic and magnetic field configuration in the MITICA

accelerator”, 27th Symp. on Fusion Technology, 2012, Belgium; submitted to Fusion Eng. Des.

[21] CHITARIN, G., et al., “Flexible Magnetic Design of the MITICA Plasma Source and Accelerator”, 3rd Int. Symp.

on Negative Ions, Beams and Sources, 2012, Finland; submitted to AIP Conf. Proc.

[22] SARTORI, E., et al., “Distribution of the background gas in the MITICA accelerator”, 3rd Int. Symp. on Negative

Ions, Beams and Sources, 2012, Finland; submitted to AIP Conf, Proc.

[23] AGOSTINETTI, P., et al., “PCCE—A Predictive Code for Calorimetric Estimates in actively cooled components

affected by pulsed power loads”, Fusion Eng. Des. 86 (2011) 1209

[24] VELTRI, P., et al., “Evaluation of power loads on MITICA injector components”, 27th Symp. on Fusion

Technology, 2012, Belgium; submitted to Fusion Eng. Des.

[25] VELTRI, P., et al., “Characterization of the space charge compensation of negative ion beams”, 3rd Int. Symp. on

Negative Ions, Beams and Sources, 2012, Finland; submitted to AIP Conf. Proc.

[26] PILAN, N., et al., “Voltage holding prediction in multi electrode-multi voltage systems insulated in vacuum”, IEEE

Trans. Diel. El. Insul. 18 (2011) 553

[27] DE LORENZI, A., et. al., “HVPTF—The high voltage laboratory for the ITER Neutral Beam test facility”, Fusion

Engineering and Design 86 (2011) 742

[28] DAY, CH. Et al., “Design progress for the ITER torus and neutral beam cryopumps”, Fusion Engineering and

Design 86 (2011) 2188

[29] LUO, X., et al., “3D Monte Carlo vacuum modeling of the neutral beam injection system of ITER”, Fusion

Engineering and Design 85 (2010) 1446