A Sirinelli

C Bourdelle

C F Maggi

E Delabie

E R Solano

F Rimini

G Dif-Pradalier

Jet-Efda

M Brix

N Fedorzack

N Hawkes

P Tamain

Ph Ghendrih

R Sabot

X Garbet

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Dynamic of density profiles in JET during slow L-H transition 
R. Sabot1, Ph Ghendrih1, A. Sirinelli2, P. Tamain1, C. Bourdelle1, M. Brix2; G. Calabro3, E. 
Delabie4, G Dif-Pradalier1, N. Fedorzack1, X. Garbet1, N. Hawkes2, C.F. Maggi5, 
F. Rimini2, E.R. Solano6,7 and JET-EFDA contributors* 
JET-EFDA, Culham Science Centre, Abingdon, OX14 3DB, UK 
1CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France; 2CCFE/Fusion Association, 
Culham Science Centre, OX14 3DB, Abingdon, UK; 3Associazione EURATOM-ENEA, 
Frascati, Italy; 4Association EURATOM-FOM, Nieuwegein, The Netherlands; 5MPI für 
Plasmaphysik, EURATOM Association, D-85748 Garching, Germany ; 6Asociacion 
EURATOM-CIEMAT, Madrid, Spain; 7EFDA Close Support Unit, Culham, UK; 
I. Introduction 
In tokamaks, the H-mode is characterized by density and temperature pedestals that build 
up at the L-H transition. During JET 2012 campaign, discharges were carried out with a 
smooth increase of heating power to compare the L-H transition threshold in JET-C and 
JET-ILW [1]. In these discharges, plasma passed through intermediate regimes between the 
L-mode and the H-mode: divertor oscillation [2] and M-mode [3]. The divertor oscillation 
(DO) is characterized by a periodic (typ. 10 ms) oscillation of plasma radiation with an 
opposition of phase between the inner and outer sid Dα signal. Although reminiscent of the 
dithering L-H transitions [4], several features distinguish the divertor oscillations. The DO 
is an oscillation between two different plasma states: firstly the edge plasma density 
increases with low divertor radiation, secondly follows a sudden decrease of the plasma 
density with increased divertor radiation [2]. During the high plasma density phase, the 
plasma stored energy increases slightly whereas dithering cycles are periodic L-H-L 
transitions at frequency an order of magnitude higher [4].  
Improvement of reflectometry [5] data processing to reduce noise and radial jitter allows to 
follow the dynamic of the density profile during the DO. This study is preliminary; a very 
limited number of shots were processed. The observations lead us to propose a simple 
model to explain the periodic density oscillations. 
II. Oscillations of density profiles during the DO 
In the discharge 83160 shown in this paper, the DO begins with an overshoot of the density 
profiles followed by periodic oscillations at ~110 Hz during 400 ms (fig 1a). Compared to 
the average DO profile, the L-mode profile, inside R=3.76m, is lower (ne - <ne>DO <0, blue 
                                                                   
* See Appendix of F. Romanelli et al, Proc. of 24th IAEA Fusion Energy Conference 2012, San Diego, USA 
40th EPS Conference on Plasma Physics P4.136
on fig 1b). The H-mode (after 54.8s) pedestal profile is much steeper: the density inside 
R=3.76m is higher (red and yellow) while the density outside R~3.76 is lower (blue). 
  
Figure 1a: evolution of density profiles measured by reflectometry every 15 µs (shot 83160).        
1b: Density variation  		 〈n54.3    54.7〉	after subtracting the average density during the 
DO period. The H mode transition occurs around t~54.7 s. Inner Dα is also shown (black line). 
The density oscillates in phase with the inner divertor Dα signal but in opposition with outer 
divertor Dα (fig. 2a) The oscillations peak inside the pedestal re ching δn~3.1018 m-3 at 
R=3.75 m ie δn/n > 10 % (fig. 2b). They are rapidly damped furthe  inside decreasing 
below 3% or δn~1.1018 m-3 at R=3.65m and becoming difficult to detect in thecore (δn<0.5 
1018 m-3). This figure shows also that the average reflectometry and High Resolution 
Thomson Scattering [6] density profiles are in good agreement. The ~2cm radial shift is 
within the expected global uncertainty on reflectometry position due to uncertainty on 
magnetic field value B. 
  
Figure 2 a): Density profile at different radii with inner and outer side Dα signal. 2b): The average 
oscillation amplitude profile (blue, right axis) peaks near the pedestal top. The density reflectometry 
(red, left axis) and HRTS (diamonds) profiles averag d over the DO period are also shown.  
III. Dynamic of density profiles during the DO phase 
The correlation time between the density at different radius and the density at R=3.75cm 
the position of the oscillation maximum shows that: 
a) b) 
b) a)  83160
40th EPS Conference on Plasma Physics P4.136
• The oscillations start in the region of the 
maximum amplitude since all delays are 
positive.  
• Inside the pedestal, oscillations are almost 
synchronized within a small delay (δt<0.5 
ms for R<2.76 m).  
• The delay increases at the edge, the edge 
density lagging the pedestal density by 2.5 
to 3 ms.  
The inner divertor Dα signal is also delayed by 
2.5 ms with respect to the density oscillations at 
R=2.75 m. 
IV. Delayed plasma fuelling: a model for divertor oscillation? 
Observation of this delay between edge and pedestal density leads us to propose a simple 
model to explain density oscillations. Let us consider the edge (pedestal) plasma particle 
content . A single reservoir is introduced assuming that the core particle evolves on 
slower time. The particle balance for this reservoir is governed by fuelling by ionisation of 
incoming neutrals and transport losses either to the core plasma or to the SOL and the 
divertor. Let  be the incoming neutral flux with characteristic velocity  and let τ  be 
the particle confinement time in the edge plasma. The particle balance then takes the form: 

τ
 =

τ
 +


〈〉 =

τ
 
where τ stands for the time, 〈〉 is the ionisation rate and τf is the effective edge plasma 
characteristic time τ = τ

τ
 !"#$〈%&〉" &'⁄
 . τf is positive during density ramp-up.	 
In this equation, all the wall out flux as well as the gas injection reach the edge plasma and 
contribute to the incoming neutral flux  as typically in the high temperature divertor 
regime, the so-called sheath-limited regime. If a fraction of the incoming neutral flux )
*  is 
ionised in the SOL and does not reach the edge plasma, the balance equation becomes: 

τ
 =

τ
)
* 〈〉 
Assuming that the divertor screening of the incoming neutrals is typically exponential one 
then obtains after linearization:  
)
* =


)+&Δ+&
)-.̅
 
Figure 3: profile of the density oscillation 
correlation time over the DO period, the 
reference is at R=3.75m 
40th EPS Conference on Plasma Physics P4.136
Δ+& is the characteristic length of the line of flight along which neutrals can be ionised 
prior to reaching the edge plasma volume 0, .̅ is the neutral ionisation mean free path at 
the reference plasma density )-, and, most important for the present model, )+& 	is the 
characteristic density in the divertor volume. From the previous observations, we suppose 
that the SOL hence the divertor density is proportional with a delay 1+ (typ. 2.5 ms) to the 
edge particle content: )+&1 = 31  1+. The evolution equation is then: 

1
 =

τ
 3
〈〉

 	1+ 
Introducing the time normalisation ∗ = 1+ τ⁄ ,	 6∗ = 1+ τ⁄  and the normalized density 7∗ 
this system is recast in a generic delayed equation w th a single parameter:  


7∗ = 7∗∗81  7∗∗  6∗: 
This equation is a typical equation for population [7]. For 0  6∗  <
=
, it has stable 
solutions. Above the threshold 6 ≥ <
=
 oscillatory solutions are obtained, the period being 
approximately 4 times the delay. The delay of 2.5 to 3 ms between the edge and the SOL 
density deduced from the edge density profile dynamic would reproduce the 10 ms 
oscillation period of the pedestal density. Existence of a threshold might also explain the 
transition from stable (L-mode) to oscillatory densitie . 
V. Conclusion 
Pedestal density profiles steepen and flatten periodically during DO preceding the SOL and 
Dα oscillations by few milliseconds. A model based on this delay is proposed to explain the 
oscillations. Although this model gives the right range for the oscillation period, more 
elements (Zonal Flows, turbulence) are probably requi d to explain other DO 
characteristics like the light confinement increase, th  phase opposition between inner and 
outer divertor D signal. 
Acknowledgment 
This work was supported by EURATOM and carried out within the framework of the 
European Fusion Development Agreement. The views and opinions expressed herein do 
not necessarily reflect those of the European Commission. 
References 
[1] C.F. Maggi, et al, 39th EPS Plasma Phys. Conf., Stockholm (2013), O3-108.  
[2] A. Loarte et al, Phys. Rev. Lett. 83, 3657–3660 (1999) 
[3] E. Solano, et al, this conference. 
[4] E. Zohm et al, Plasma Phys. Controlled Fusion 37, 437 (1995). 
[5] A. Sirinelli et al, Rev. Sci. Instrum. 81, 10D939 (2010). 
[6] M. Kempenaars et al, Rev. Sci. Instrum. 79, 10E728 (2008) 
[7] J.D Murray Mathematical Biology I: An Introduction, 3rd ed, Springer, (2003). 
40th EPS Conference on Plasma Physics P4.136


Dynamic of density profiles in JET during slow L-H transition

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Dynamic of density profiles in JET during slow L-H transition

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