Introduction to the Diagnosis of Magnetically Confined Thermonuclear - - PowerPoint PPT Presentation

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Introduction to the Diagnosis of Magnetically Confined Thermonuclear Plasma

Core diagnostics I: Heavy Ion Beam Probe (HIBP)

• J. Arturo Alonso

Laboratorio Nacional de Fusión EURATOM-CIEMAT E6 P2.10 arturo.alonso@ciemat.es

version 0.1 (March 2, 2011)

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 1 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Outline

1

Motivation: Radial electric fields and trasnport barriers Electric fields and plasma motion Electric fields and confinement transitions Experimental determination of the radial electric field

2

The Heavy Ion Beam Probe General Principle Injection, energy analyser and measurement localisation

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 2 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Outline

1

Motivation: Radial electric fields and trasnport barriers Electric fields and plasma motion Electric fields and confinement transitions Experimental determination of the radial electric field

2

The Heavy Ion Beam Probe General Principle Injection, energy analyser and measurement localisation

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 3 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Electric fields in a quasineutral plasma

We have said that plasma has a strong tendency to remain quasineutral ne ≈ ni, or more precisely |ni − ne|/n ≪ 1 with n = 1

2(ni + ne).

However, tiny deviations from neutrality render measurable macroscopic electric fields.

• Take δ = (ni − ne)/n, then Poisson’s equation reads

∇2φ = ρ ǫ0 ⇒ d drEr = δ en ǫ0 ,

• now take n = 1019 m−3 and dEr/dr ≈ Er/a with a = 1m to

get Er((V/m)) = 1.8 × 1011δ

A deviation from neutrality δ = 10−9 would cause an electric field of ∼ 100V/m.

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 4 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Ambipolar electric field

The electron and ion cross-field fluxes Γe,i are functions of the radial electric field Er. These two fluxes need not be the same, but whenever there is a preferential loss of charge, an electric field will build up to equilibrate the losses and preserve the plasma quasineutrality. The equilibrating radial electric field is called ambipolar field and, for a two species (e, i) plasma, is given by the condition Γe(Er) = Γi(Er) This equation is the basis of most calculations of the equilibrium Er in a plasma

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 5 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

The E × B drift

The fluid velocity of an isotropic and frictionles plasma (m, q)-specie evolves acroding to mn(∂tu + u · ∇u) = −∇p + qn(E + u × B) (1) Neglect inertial forces (drift ordering δ = ρ/L ≪ 1) and multiply by B×(1) u⊥ = E × B B2 + ∇p × B nqB2 = uE + u∗. A radial electric field Er causes a plasma-fluid rotation perpendicular to the magnetic field and contained within the flux surface

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 6 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

L to H transition

Low confinement mode (L-mode) was the only mode before the 80’s Characterised by strong turbulent transport and power degradation Above a Pth the plasma suddenly transits to a improved mode of confinement (H-mode) where τ (H)

E

∼ 2τ (L)

E . L to H transition is not

yet understood!! H-mode and the edge transport barrier Turbulence supression by shear decorrelation Also ITBs (Advanced Scenarios).

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 7 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

L to H transition

Low confinement mode (L-mode) was the only mode before the 80’s Characterised by strong turbulent transport and power degradation Above a Pth the plasma suddenly transits to a improved mode of confinement (H-mode) where τ (H)

E

∼ 2τ (L)

E . L to H transition is not

yet understood!! H-mode and the edge transport barrier Turbulence supression by shear decorrelation Also ITBs (Advanced Scenarios).

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 7 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

L to H transition

Low confinement mode (L-mode) was the only mode before the 80’s Characterised by strong turbulent transport and power degradation Above a Pth the plasma suddenly transits to a improved mode of confinement (H-mode) where τ (H)

E

∼ 2τ (L)

E . L to H transition is not

yet understood!! H-mode and the edge transport barrier Turbulence supression by shear decorrelation Also ITBs (Advanced Scenarios).

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 7 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

L to H transition

Low confinement mode (L-mode) was the only mode before the 80’s Characterised by strong turbulent transport and power degradation Above a Pth the plasma suddenly transits to a improved mode of confinement (H-mode) where τ (H)

E

∼ 2τ (L)

E . L to H transition is not

yet understood!! H-mode and the edge transport barrier Turbulence supression by shear decorrelation Also ITBs (Advanced Scenarios).

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 7 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

L to H transition

Low confinement mode (L-mode) was the only mode before the 80’s Characterised by strong turbulent transport and power degradation Above a Pth the plasma suddenly transits to a improved mode of confinement (H-mode) where τ (H)

E

∼ 2τ (L)

E . L to H transition is not

yet understood!! H-mode and the edge transport barrier Turbulence supression by shear decorrelation Also ITBs (Advanced Scenarios).

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 7 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

L to H transition

Low confinement mode (L-mode) was the only mode before the 80’s Characterised by strong turbulent transport and power degradation Above a Pth the plasma suddenly transits to a improved mode of confinement (H-mode) where τ (H)

E

∼ 2τ (L)

E . L to H transition is not

yet understood!! H-mode and the edge transport barrier Turbulence supression by shear decorrelation Also ITBs (Advanced Scenarios).

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 7 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

L to H transition

Surface radius P l a s m a P r e s s u r e H-mode (Advanced Scenarios) Internal Transport Barrier

Low confinement mode (L-mode) was the only mode before the 80’s Characterised by strong turbulent transport and power degradation Above a Pth the plasma suddenly transits to a improved mode of confinement (H-mode) where τ (H)

E

∼ 2τ (L)

E . L to H transition is not

yet understood!! H-mode and the edge transport barrier Turbulence supression by shear decorrelation Also ITBs (Advanced Scenarios).

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 7 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Experimental determination of Er

Because of these and other things it is very interesting to measure radial electric fields in fusion plasmas. Sevela diagnostics are used for that: Langmuir probes (only for the far SOL in hot H-mode plasmas) Impurity (s) line doppler broadenning (Ts) and shift (vs). From the velocity expression u⊥ = E × B B2 + ∇ps × B nsqsB2 ⇒ Er = − 1 nsqs dps dr + vϕsBθ − vθsBϕ . Heavy Ion Beam Probe – direct measurement

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 8 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Outline

1

Motivation: Radial electric fields and trasnport barriers Electric fields and plasma motion Electric fields and confinement transitions Experimental determination of the radial electric field

2

The Heavy Ion Beam Probe General Principle Injection, energy analyser and measurement localisation

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 9 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

General principle

1 Heavy ions are injected into

the plasma at a known energy

2 Ions collide with plasma

electrons and get further ionised

3 They are deflected away from

the primary beam and their energy is measured

4 From the difference in the

injection and detection energy we can infer the electric potential at the ionization point (sample volume)

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 10 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Formal derivation of φ

The Hamiltonian of a charge in an electromagnetic field is H(x, p, t) = 1 2m(p − qA)2 + qφ = 1 2mv2 + qφ = Ek + Ep The Hamiltonian equations give x(t), p(t). In the absence of any other forces the total energy (hamiltonian) variation between tA and tB is ∆H = tB

tA

dH dt dt = tB

tA

∂H ∂t dt , where we have used the hamiltonian property dH

dt = ∂H ∂t .

Using the Hamiltonian expression we obtain ∆H(A → B) = q tB

tA

∂φ ∂t dt − q tB

tA

v · ∂A ∂t dt ≡ qΩAB .

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 11 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Formal derivation of φ

1 The change of the ion’s energy

between A and B is ∆H(A → B) = qΩAB

2 Electron impact ionization

changes q → q + e and therefore ∆H(B) = eφ(B) (mi ≫ me so the collision does not change the ion’s kinetic energy).

3 From B to C again free flight

∆H(B → C) = (q + e)ΩBC

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 12 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Formal derivation of φ

1 The change of the ion’s energy

between A and B is ∆H(A → B) = qΩAB

2 Electron impact ionization

changes q → q + e and therefore ∆H(B) = eφ(B) (mi ≫ me so the collision does not change the ion’s kinetic energy).

3 From B to C again free flight

∆H(B → C) = (q + e)ΩBC

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 12 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Formal derivation of φ

1 The change of the ion’s energy

between A and B is ∆H(A → B) = qΩAB

2 Electron impact ionization

changes q → q + e and therefore ∆H(B) = eφ(B) (mi ≫ me so the collision does not change the ion’s kinetic energy).

3 From B to C again free flight

∆H(B → C) = (q + e)ΩBC

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 12 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Formal derivation of φ

4 The total energy increment

A → C is then ∆H(A → C) = qΩAB + eφ(B) + (q + e)ΩBC

5 Solving for the electric potential φ

eφ(B) = HC −HA −(qΩAB +(q+e)ΩBC) .

6 Using φ(A) = φ(C) = 0 and

neglecting field variations (Ω) eφ(B) = Ek,C − Ek,A .

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 13 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Formal derivation of φ

4 The total energy increment

A → C is then ∆H(A → C) = qΩAB + eφ(B) + (q + e)ΩBC

5 Solving for the electric potential φ

eφ(B) = HC −HA −(qΩAB +(q+e)ΩBC) .

6 Using φ(A) = φ(C) = 0 and

neglecting field variations (Ω) eφ(B) = Ek,C − Ek,A .

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 13 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Formal derivation of φ

4 The total energy increment

A → C is then ∆H(A → C) = qΩAB + eφ(B) + (q + e)ΩBC

5 Solving for the electric potential φ

eφ(B) = HC −HA −(qΩAB +(q+e)ΩBC) .

6 Using φ(A) = φ(C) = 0 and

neglecting field variations (Ω) eφ(B) = Ek,C − Ek,A .

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 13 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Heavy ion injection

Injected ions need to have sufficiently large Larmor radius rL = mv⊥ qB = √2mE⊥ qB

• Need to have large mass (Cs+(133), Tl+(204)) and injection

energy (from 10kV to 2MV)

• In TJ-II: Cs+ at 130 kV ⇒ v =
• 2E/m ≈ 400 km/s, i.e.

crosses the vacuum vessel in 2 µs.

• The larger B the more the injection energy required (for this

reason is unpractical for large B like in JET or ITER)

Ion source is a zeolite (microporous mineral) impregnated with the chosen element. Ions are released by heating and accelerated by an electrostatic potential. Typical beam parameters are I ∼ 100µA and diameter ∼ 1cm (measurement localization).

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 14 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

The Proca-Green energy analyser

High accuracy: needs to detect ∼ 10V in 130, 000V Beam deflection in a constant E-field is a function of its energy Ek = qSVA (G(θI) + F(θI)δi) , δi = iu − id iu + id , φ(B) = 2VA (G(θI) + F(θI)δi) − VI .

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 15 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Sample volume: Trajectory back-tracing

Once φ(B) is known one needs to calculate the spatial location of the SV → intersection of primary and secondary trajectories in a known B.

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 16 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Other plasma quantities

While the electric potential measurement is the distinguishing feature of the HIBP it can also give some other information. The secondary generation is caused by electron impact and the secondary current is Is = qsVsvneniσv(Te) ∝ ne , although for high ne the beam gets atenuated along the path. The side deflection of the secondary beam can be related to the ‘poloidal’ B-field and plasma current density (very non-trivial).

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 17 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Practical implementations

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 18 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Sample measurements

TJ-II stellarator [A. Melnikov et al.]

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 19 / 20

Motivation: Radial electric fields and trasnport barriers The Heavy Ion Beam Probe

Sample measurements

CHS stellarator [Fujisawa et al.]

Core diagnostics I: Heavy Ion Beam Probe (HIBP), A. Alonso, copyleft 2010 20 / 20