Alpha Particle Transport due to

Inelastic Atomic Processes

C. F. Clauser and R. FarengoBariloche Atomic Centre and Balseiro Institute, National Atomic Energy Commission, Argentina.

cesar.clauser@ib.edu.ar

Atomic processes that changes the alpha particle

charge can produce a large transport in the

plasma edge-SOL regions

Fussmann [1] studied this process for alpha particles in

the central (core) region and concluded it was not

important.

We showed [2] that large diffusion coefficients are

obtained for parameters typical of the pedestal, edge and

SOL regions. The (inverse) gradient of the neutral density

produces a large inward flux.

Collisions with cold D and He and plasma particles are

considered. Other processes (i. e. collisions with partially

ionized Be, W) should be included. Data is limited.

To calculate the transport of fusion born alpha particles in a realistic non uniform

background we developed a numerical code that follows the exact particle trajectories

by solving Newton’s equation:

Processes that reduce the charge Processes that increase the charge

Analytical calculation of the local diffusion coefficient possible for monoenergeticparticles [1], [2].

References[1] G. Fussmann. Contrib. to Plasma Phys. 37, 363 (1997).

[2] C. F. Clauser and R. Farengo, Phys. Plasmas 22, 122502 (2015).

[3] IAEA AMDIS ALADDIN Database: https://www-amdis.iaea.org/ALADDIN/

[4] C. F. Clauser and R. Farengo, Nucl. Fusion 57, 046013 (2017).

Realistic ITER equilibrium and density and temperature profiles

The initial velocity distribution of the alpha particles is an isotropic slowing down distribution function, while thespatial distribution has a Gaussian shape. No sources included. Only the region with r>0.6 simulated [4].

Uniform plasma (𝒏𝒆 = 𝟏𝟎𝟐𝟎𝐦−𝟑, 𝑻𝒆 = 𝟒 𝐤𝐞𝐕) andneutral background (𝒏𝒏 = 𝟎. 𝟑𝟓 × 𝟏𝟎𝟏𝟖𝐦−𝟑).Large diffusion coefficient for low neutral density

Non uniform neutral density (𝒏𝒏𝟎 = 𝟏% 𝒏𝒆 ). Arapid displacement opposite to the neutral densitygradient appears (inward flux).

Particles that cross the dashed red line assumed to be lost to the divertor.

Atomic processes are very important in the pedestal-edge-SOL region

and should be included in calculations of the alpha particles flux and

the power deposited in the wall and divertors.

Uniform neutral density (0.5%). Large increase of the

loss rate (black curve), as expected.

Non-uniform neutral density. A reduction of the

stationary loss rate is observed due to the inward flux.

Density profiles at

30 ms.

A non uniform neutral density profile (increasing towards the wall) reduces the

loss rate below the neoclassical value and modifies the 𝜶-particles density.

Elastic (Coulomb) collisions: almost all the lost particles reach the divertor. The lost particles have

very low energy (close to the plasma energy).

Elastic+inelastic collisions: a large fraction (𝟑𝟐. 𝟏% for 𝒏𝒏 = 𝟏% ) reach the wall. The energy

distribution of lost particles peaks around 400 keV.

With inelastic collisions, the region near the

separatrix is depleted of alpha particles and

a gentle bump appears for 0.80<r<0.90.

Total cross sections were obtained from the ALADDIN Database [3]

The collision frequency of a process measures its relevance

Collision frequencies

𝜈𝑞1→𝑞2𝛼𝛽

= 𝑛𝛽 𝜎𝑣 𝑞1→𝑞2

𝛼𝛽= 𝑛𝛽 𝑑𝐯𝛽𝑓𝛽 𝐯𝛽 𝜎 𝑣𝑟 𝑞1→𝑞2

𝛼𝛽𝑣𝑟

Numerical Code

Plasma electrons and deuterons are described with a Maxwell-Boltzman distributionfunction. Other species (which we called “neutrals”) are considered cold.

D ≈ 𝑣⊥2𝜈2→1

Ω22 +

𝜈2→1𝜈1→0

𝜈0→12 𝜈1→2

𝜈𝑞1→𝑞2 =

𝛽

𝜈𝑞1→𝑞2𝛼𝛽

cross section for collisions between 𝛼 and 𝛽 (target) particles that produces acharge change from 𝑞1 to 𝑞2.𝜎 𝑣𝑟 𝑞1→𝑞2

𝛼𝛽

1D case. Uniform magnetic field. Only inelastic collisions.

The effect of inelastic collisions is introduced via a Monte Carlo type operator.

The probability of each process is proportional to its frequency.

Elastic (Coulomb) collisions are also included ( 𝑣𝛼,𝑒𝑐).

The code runs on a GPU and was checked by recovering the analytic results.

𝑑𝐯𝛼𝑑𝑡

=𝑞 𝑡

𝑚𝛼𝐯𝛼 × 𝐁 + 𝑣𝛼,𝑒𝑐

𝐏𝐫𝐨𝐛𝑞1→𝑞2 ≈ 𝜈𝑞1→𝑞2Δ𝑡

Reference values are:

𝑻𝒆𝟎 = 𝟐𝟓 𝐤𝐞𝐕 𝒏𝒆𝟎 = 𝟏𝟎𝟐𝟎𝐦−𝟑

𝒏𝒏𝟎 𝒏𝒆𝟎 = 𝐚 𝟎. 𝟏%, 𝐛 𝟏%, 𝒄 𝟓%

Studies were performed with only elastic collisions (EC) and with both elastic andinelastic collsions (EC+IC)

Inelastic collisions modify spatial distribution of lost particles.

Inelastic diffusion

Particle rotating in a uniform magnetic field. Charge

changes produce jumps in the guiding centre position.

Processes that reduce the charge Processes that increase the charge

Up to 𝟒 × 𝟏𝟎𝟓 particles were simulated.

𝜶+𝟐+𝐃𝟎→𝜶++𝐃+

𝜶+𝟐+𝐃𝟐𝟎→𝜶++𝐃𝟐

+

𝜶+𝟐+𝐇𝐞𝟎→𝜶++𝐇𝐞+

𝜶+𝟐+𝐇𝐞+→𝜶++𝐇𝐞+𝟐

𝜶++𝐃𝟎→𝜶𝟎+𝐃+

𝜶++𝐃𝟐𝟎→𝜶𝟎+𝐃𝟐

+

𝜶++𝐇𝐞𝟎→𝜶𝟎+𝐇𝐞+

𝜶++𝐇𝐞+→𝜶𝟎+𝐇𝐞+𝟐

𝜶++𝒆−→𝜶+𝟐+𝒆−+𝒆−

𝜶++𝐃+→𝜶+𝟐+𝐃𝟎

𝜶++𝐃+→𝜶+𝟐+𝐃++𝒆−

𝜶++𝐇𝐞+→𝜶+𝟐+𝐇𝐞𝟎

𝜶𝟎+𝒆−→𝜶++𝒆−+𝒆−

𝜶𝟎+𝐃+→𝜶++𝐃𝟎

𝜶𝟎+𝐃+→𝜶++𝐃++𝒆−

𝜶𝟎+𝐃𝟐𝟎→𝜶++𝐃𝟐

𝟎+𝒆−

𝜶𝟎+𝐇𝐞+→𝜶++𝐇𝐞𝟎