# Preliminary Design of Alborz Tokamak

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## Abstract

The Alborz tokamak is a D-shape cross section tokamak that is under construction in Amirkabir University of Technology. The most important part of the tokamak design is the design of TF coils. In this paper a refined design of the TF coil system for the Alborz tokamak is presented. This design is based on cooper cable conductor with 5 cm width and 6 mm thickness. The TF coil system is consist of 16 rectangular shape coils, that makes the magnetic field of 0.7 *T* at the plasma center. The stored energy in total is 160 kJ, and the power supply used in this system is a capacitor bank with capacity of *C* = 1.32 mF and *V*_{max} = 14 kV.

### Keywords

Toroidal field Toroidal coil Aspect ratio Major and minor radius FEM## Introduction

The tokamak is a toroidal plasma confinement system, the plasma being confined by a magnetic field. The principal magnetic field is the toroidal magnetic field [1]. Alborz tokamak is a D-shape cross section tokamak and the most important part of the design of this tokamak is the design of TF coils and its power supply.

Some tokamaks has circular cross section [2, 3] but many of advanced tokamaks have typically D-shape or non-circular cross section [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19] and some of them has superconducting field coils [12, 13, 14, 15, 16, 17, 18, 19, 20].

In this paper we are present the design of TF coils and give the major parameters of tokamak like major radius, maximum plasma current, number of TF coils, number of total turns and current per turn for a non-circular cross section TF coil. And we assume that some of the parameters like maximum current carrying by the cooper cable, the capacity of the power supply, maximum operational voltage, required safety factor, aspect ratio and the cross section shape of vacuum vessel and the toroidal magnetic field in plasma center, are known.

In addition we must consider about the magnetic field ripple. The magnetic field ripple is inversely proportional to the number of TF coils and by increase of their number is decreased [21]. Number of TF coils is normally about 12–36 coils [22, 23]. The ripple magnitude due to the finite number of TF coils and the size of the ports of vacuum vessel, determine the number, size and shape of TF coils [24]. Axisymmetry of magnetic field topology insures good classical particle confinement. However, due to discreteness of the TF coil system, it is unavoidable to have some ripple component in the toroidal magnetic field [24, 25].

The TF coils are wound around the vacuum vessel. The vacuum vessel provides a suitable condition for plasma shaping, baking, confinement, stability and supervising [22, 23, 26].

In some tokamaks for investigate of toroidal field behavior, use a detailed Finite Element Method (FEM) [7, 27, 28, 29] and in this paper we use a detailed 3D finite element method for all component of TF coils.

## Calculation of Major and Minor Radius and Turn Numbers of TF Coils

*A*=

*R*/

*a*= 3). We expect that the toroidal magnetic field at the center of the vacuum vessel is 0.7

*T*. The power supply used in this system is a capacitor bank of 1.32 mF, and

*V*

_{max}= 14 kV that has energy of \( E = \frac{1}{2} \)

*CV*

^{2}= 129 kJ. Currently, the range of safety factor on the edge of plasma for stable operation of tokamaks is usually between 3 and 4, while it takes on a minimum value of unity at the axis of plasma due to nonlinear sawtooth oscillation [30]. To satisfy this criteria, we set the safety factor 3 (

*q*= 3). The coil material is cooper and it’s area is 5 cm × 6 mm, that can carry 12 kA of transient current, that is

*I*

_{max}= 12 kA. Thus the circuit diagram of power supply and TF coils is depicted in Fig. 1, that

*V*is the power supply voltage.

*S*is closed, the stored energy in

*C*transfer to

*L*, and gives

*C*= 1.32 mF,

*V*

_{max}= 14 kV,

*I*

_{max}= 12 kA, gives

*B*

_{T}is toroidal magnetic field,

*N*is the number of turns,

*I*is turn’s current, and

*R*is major radius.

*I*= 12 kA,

*B*

_{T}= 0.7

*T*, and

*R*= 3

*a*gives

*N*turn is

*r*is minor radius of coil. For insulation and assembly pieces and to avoid of sharp variation of magnetic field of adjacent coils, we put a distance of 5 cm between coils and vacuum vessel. And since the width of cable is 5 cm, the minor radius of TF coils is

## Winding of TF Coils

Thus the number of coils is 16 and the number of turns per coils is 10.

We must consider that every coil consist of 10 turns.

## Calculation of Plasma Current

*B*

_{θ}is poloidal magnetic field and

*I*

_{p}(

*r*) is plasma current

*j*(

*r*′) is the current density inside

*r*, and by using the

*r*=

*a*, the edge value of

*q*is

*q*= 3, the maximum value of

*I*

_{p}is

Parameters of Alborz tokamak

Parameters | Value |
---|---|

Toroidal magnetic field (in | 0.7 |

Minor radius (m) | 0.15 |

Aspect ratio | 3 |

Edge safety factor | 3 |

Maximum plasma current (kA) | 116 |

Number of TF coils | 16 |

Number of total turns | 160 |

Total stored energy (kJ) | 129 |

Current per turn (kA) | 12 |

## Simulation of Toroidal Magnetic Field

^{′}and 11.25

^{′}. (a) is in 0

^{′}and (b) is in 11.25

^{′}, that is between coils.

*R*.

Toroidal field in *R*_{o} = 0.45 m is 0.85 *T*.

## Summary

*C*= 1.32 mF and

*V*

_{max}= 14 kV as toroidal coils power supply, and by consider of cooper coils with area of 0.05 × 0.006 m

^{2}, we gives

*I*

_{max}= 12 kA, that gives a tokamak with

*R*

_{o}= 0.45 m,

*a*= 0.15 m, and

*B*

_{T}= 0.85

*T*. This tokamak is under construction in Amirkabir university of technology. The expected parameters of this tokamak is shown in Table 2.

Expected parameters of Alborz tokamak

Parameters | Value |
---|---|

Toroidal magnetic field (in | 0.85 |

Minor radius (m) | 0.15 |

Aspect ratio | 3 |

Edge safety factor | 3 |

Maximum plasma current (kA) | 141 |

Number of TF coils | 16 |

Number of total turns | 160 |

Total stored energy (kJ) | 129 |

Current per turn (kA) | 12 |

## Open Access

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