A new experimental classification of divertor detachment in ASDEX Upgrade

In this paper, a new experimental classification of divertor detachment in ASDEX Upgrade is presented. For this purpose, a series of ohmic and L-mode density ramp discharges at different heating powers, magnetic field directions and plasma species were carried out. For the first time at ASDEX Upgrade the electron density in the divertor volume and the occurrence of volume recombination were measured by means of spectroscopy. It is shown that detachment is not a continuously evolving process but rather undergoes three distinct states while the characteristics of the inner and outer divertor are strongly coupled. Before the complete detachment of the inner and outer divertor, radiative fluctuations occur in the inner divertor close to the X-point, observed for the first time via new fast diode bolometers. Finally, the effect of an externally applied magnetic perturbation field on the detachment process is investigated.


Introduction
Avoiding damage of the divertor material by keeping the power load below a certain threshold is a major challenge of future fusion devices such as ITER. For tungsten, at least in the D-T campaign, the foreseen ITER divertor target material, the power load must be kept below P ≈ 10 MW m −2 in continuous operation. This can only be achieved in ITER with the plasma being detached or partially detached [1,2]. Divertor detachment is characterized by a strong reduction in the total particle flux to the target plates. With a reduction in the plasma temperature in front of the target volumetric processes become important [3][4][5]. At electron temperatures below ≈5 eV recycled neutrals from the target undergo several charge exchange (CX) collisions with plasma ions before they are ionized. This results in a change from a free-streaming to a diffusive-like plasma flow towards the target, which leads to a broadening of the ion flux profile at the target. Although the total ion flux is not reduced by CX collisions, a reduction in the peak ion flux is achieved. Furthermore, at T 1.5 eV plasma ions can recombine before reaching the target. This process leads to a strong reduction in the total ion flux and plasma pressure and to an increase in the neutral pressure in front of the target. The necessary temperature reduction can be achieved by increasing the plasma density via fuelling or with an additional injection of impurities, which cool the divertor plasma via line radiation.
Plasma detachment has been experimentally investigated in many tokamaks and the qualitative mechanisms leading to detachment seem to be understood [6][7][8]. A theoretical description of the detachment process is based on strongly coupled nonlinear equations and a quantitative description is only possible through extensive code simulations. But even the most sophisticated codes are not able to reproduce all experimental observations related to divertor detachment of present-day experiments [9], indicating that there might be some physical processes missing in the codes. In particular, to be able to predict the ITER divertor performance a correct simulation of divertor detachment is indispensable.
For example, the onset of detachment, defined by the moment when the ion flux to the target starts to decrease as the plasma density is further increased (the so-called rollover), happens in most tokamaks much earlier in the inner than in the outer divertor. Moreover, the inner divertor receives a higher ion flux and a lower power load before the onset of detachment compared with the outer divertor. Several reasons for these asymmetries have been discussed [10][11][12][13][14]. At present, it is thought that they are primarily caused by drift flows [15,16]. Furthermore, the radial transport of plasma particles in the scrape-off layer (SOL) is unknown. In the codes it is usually assumed to be of diffusive nature. But it was shown that at medium to high densities intermittent turbulent transport can be dominant [17] and increases with density [18]. Hence, in a recent work a collisionality-dependent diffusion coefficient D ⊥ was used instead of a constant one [19]. This yields better results with respect to the density where the rollover occurs.
A key to an improved description of detachment is a better knowledge of the plasma parameters in the divertor and the SOL. The aim of this paper is the detailed characterization of divertor detachment with new diagnostics available at ASDEX Upgrade. We present the spatio-temporal evolution of detachment in both, the inner and outer divertor. For this purpose, a series of ohmic and L-mode discharges were performed where detachment was achieved through density ramps. The experiments were carried out at different heating powers, magnetic field directions and plasma species. For the first time the electron density in the divertor volume and the occurrence of volume recombination were measured by means of spectroscopy. It is shown that detachment in ASDEX Upgrade is not a continuous process but rather undergoes three distinct states while the characteristics of the inner and outer divertor are strongly coupled. The paper is organized as follows: in section 2, an overview of the experimental and diagnostic setup is given and methods determining the occurrence of volume recombination and the magnitude of detachment are introduced. The evolution of the detachment process is presented in detail in section 3. Section 4 discusses phenomena, which are observed here for the first time and a summary is given in section 5.

Discharge setup
A series of ohmic and L-mode density ramp discharges has been performed at ASDEX Upgrade to study the detachment of the divertor. Since 2007, the plasma-facing surfaces of ASDEX Upgrade are completely covered with tungsten [20]. All discharges of this series were in lower single null divertor configuration with a lower triangularity of δ = 0.36, a plasma current of I p = 1 MA, a toroidal magnetic field of B t = 2.5 T and a safety factor of q 95 ≈ 4. The electron cyclotron resonance heating, ECRH, power was varied from discharge to discharge. The fuelling species was changed between deuterium and hydrogen and the field direction was changed between forward field (ion B × ∇B drift towards the lower divertor) and reversed field, see table 1. Due to the alignment of the divertor tiles, the magnetic helicity cannot be reversed. Thus, B t and I p have to be changed simultaneously in reversed field operation. In addition, one discharge was performed with an externally applied magnetic perturbation field (MP), see table 1.
In figure 1 time traces of various plasma parameters for the discharge #27100 are shown. The current flat top was reached  figure 2, with the inner and outer SOL or high and low field side divertor SOL, respectively. The strike point positions had to be kept constant to measure the temporal evolution of the divertor plasma excluding any geometric effect. The gas fuelling ramp starts at 2 s and was increased from 1 × 10 21 up to 1 × 10 22 atoms s −1 with a rate of 1 × 10 21 atoms s −2 . Then the rate was increased to 3 × 10 21 atoms s −2 and the fuelling was ramped up until the density limit occurred. The fuelling ramp leads to a continuous increase in the plasma density and to the development of the detachment in the divertor. The same fuelling scheme was used for all discharges.

Diagnostic setup
Flush mounted Langmuir triple probes (LP) measure the ion saturation current density, j sat , and the electron density, n e,t , and temperature, T e,t , at the divertor targets at the positions shown in figure 2(a). The ion flux, D + , is then calculated dividing j sat by the elementary charge e, assuming pure deuterium plasmas. The spatial probe separation in the poloidal direction is ≈2 cm in the inner and ≈2.5 cm in the outer divertor. The acquisition time is t = 0.035 ms.
The electron density in the divertor volume, n e,V , is determined via a spectroscopic measurement of the Starkbroadened D line. This method is commonly used on other devices, such as JET, MAST or C-Mod [8,21,22]. Here, synthetic Stark-broadened line shapes, calculated and published by Stehlé [23] based on the model microfield method, are convoluted with the instrument function and the Doppler broadening of a fixed neutral temperature of T n = 5 eV. These shapes are fitted to the measured lines in a least-squares sense, in which n e,V is a fit parameter. For n e,V 4 × 10 19 m −3 and B t 3 T the Zeeman splitting and variations of T n can be neglected (for details see [24]). This measurement has an uncertainty of 15%, an acquisition time of t = 2.65 ms and is a line-integrated measurement weighted with the D emissivity along the lines of sight (LOS) which are shown in figure 2. Together with the crossed LOS the measurement can approximately be localized by comparing it with the total radiation distribution measured by bolometry. If recombination processes can be neglected, the D emission profile is comparable to the distribution of the total radiation. Recombination preferably populates the higher n-levels. Thus, if recombination is dominant, the D emission is not comparable anymore to the total radiation, which is still dominated by ionization processes.
Fast AXUV diode bolometers measure the radiation between 1 eV and 8 keV [25]. This measurement is not absolutely calibrated and has a time resolution of 5 µs. The positions of the the bolometer chords are shown in figure 2(b).

Spectroscopic determination of volume recombination
By measuring the line emission ratio of two different transitions of the same atom it is, in principle, possible to determine the electron temperature. Therefore, it is necessary that the line emissions of both transitions weakly depend on the electron density. For example, this is routinely done at TEXTOR by measuring helium line ratios [26] or at JT-60U and JET by measuring Balmer line ratios [27,28]. With the spectrometers used for this work, it is possible to measure the Balmer D δ and D lines simultaneously. As these are lineintegrated measurements, our aim was not to deduce absolute temperatures out of the D δ /D ratio, but to deduce whether the divertor plasma is dominated by ionization or recombination.
The emissivity of the Balmer D δ line, n = 6 → n = 2, is written as 6→2 = n e n +0 D PEC exc (n e T e ) + n e n +1 D PEC rec (n e T e ) = n e n D f +0 PEC exc (n e T e ) + f +1 PEC rec (n e T e ) TEC (1) with n +0 D and n +1 D the neutral deuterium and ionized deuterium densities, respectively. The PECs are the so-called photon emissivity coefficients for recombination and excitation and have been calculated for various elements and transitions by the ADAS project 1 based on a collisional-radiative model [29]. The PEC exc and PEC rec are illustrated in figure 3(a) for two different densities. It can be seen that the recombination process dominates with respect to ionization when T < 1.5 eV.
The fractional abundance, f , in equation (1) is the ratio of the neutral or ionized deuterium density to the total deuterium density n D : f +0,+1 = n +0,+1 /n tot . Figure 3(b) shows the fractional abundance for two different densities. Below T ≈ 1.5 eV almost all deuterium atoms are in the neutral state.
For the calculation of f transport effects are neglected and only the balance of ionization and recombination rates is taken into account. The neglected transport effects will lead to a modification of the curves, but the transition from neutral to ionized deuterium is always around ≈ 1.5 eV.
The expression in the brackets in equation (1) is called the total line emission coefficient (TEC) here and is shown in figure 3(c) for two different densities. The TEC peaks at T e ≈ 1.5 eV and drops rapidly when the temperature decreases. This is due to the strong decrease in the ionized deuterium density (figure 3(b)) as the plasma is dominated by recombination ( figure 3(a)). Moreover, the TEC has almost no dependence on the electron density. The line emission ratio of D δ and D is the ratio of the corresponding TECs and given by equation (1): where the electron and total hydrogen densities cancel out. Figure 3(d) shows D δ /D for two different densities. The line ratio depends weakly on the electron density and increases strongly at T e < 1 eV when recombination becomes dominant. Due to this strong increase in the line ratio and the flat profile above 1 eV we can determine whether recombination is the dominant process or not.

The two-point model and the degree of detachment
For the conduction-limited regime there exists a set of simplified equations, which describe the relation between the upstream and target parameters, called the two-point model (TPM) [30]: where n sep and q sep are the upstream separatrix density and heat flux density entering the SOL, respectively, L c is the connection length from upstream towards the target, κ 0e is the electron heat conductivity, γ is the sheath heat transmission coefficient and m i is the ion mass. The power loss factor (0 < f pow < 1), the momentum loss factor (0 < f mom < 1) and the convection factor (0 < f conv < 1) account for the power and momentum which are lost and the fraction of power which is convected along a field line towards the target, respectively. The simplest case neglecting all loss factors (f conv = f mom = f pow = 0) is called the simple TPM [31]. Similar to a previous work at JET [32] we use the notation of the degree of detachment (DOD), which is defined as the ratio of the calculated ( calc D + ) and measured ( meas D + ) ion flux to the target. According to the TPM the ion flux reaching the divertor target is proportional to the square of the upstream separatrix density n sep (equation (5)). Furthermore, for ohmic and L-mode discharges it has been shown that n sep u scales approximately linearly with the line-integrated plasma density, n e [33]. Therefore we deduce calc D + from a horizontal edge interferometer measurement (figure 1(c)) and the DOD is then calculated as The total ion flux to the entire target is obtained by integrating over all LP measurements along the divertor surface: where the S coordinate is the distance from the strike point along the divertor surface in the poloidal direction, positive values are in the SOL (see figure 2(a)). It should be noted that the large separation between the third and the second uppermost probe in the inner divertor (figure 2(a)) results in an additional uncertainty of meas D + . When the divertor plasma can be described by the simple TPM, then calc D + = meas D + and DOD = 1. The main assumptions of the model are that there is no significant energy and pressure loss along a field line. Simply speaking, when the pressure drops along a field line, hence detachment begins, meas D + becomes less than calc D + and DOD > 1. There could be other mechanisms leading to a weaker rise in meas D + compared with the TPM scaling such as, e.g., a change in the ratio between conducted and convected parallel heat flux or an increase in the radial transport. The linear dependence between the separatrix and the edge density might also change within one discharge during a density ramp. Therefore, for our work we define the onset of detachment when meas D + rolls over and use the DOD just as a guideline for the magnitude of detachment.

Evolution of divertor detachment-the three detachment states
The main observation of this work is that the detachment process can be divided into three different states. In the first state, which we will call the onset state (OS), the first deviation from the simple TPM scaling happens. In the second one, called the fluctuating state (FS), radiative fluctuations in the inner SOL close to the X-point occur [34]. When these fluctuations vanish, complete detachment over a large target area sets in simultaneously in the inner and outer divertor, giving this third state the name complete detachment state (CDS). Furthermore, the characteristics of these states are a combination of both the inner and outer divertor conditions, meaning that the behaviour of both divertors is coupled. These divertor conditions will be described in detail in the following for the forward field direction with deuterium fuelling (section 3.1), for the forward field direction with hydrogen fuelling (section 3.2) and for the reversed field direction with deuterium fuelling (section 3.3).

The three detachment states in forward field
In the following, we describe the evolution of detachment in the inner and outer divertor in the forward field direction with deuterium as the main ion species. Representative for all discharges of this series, which are made in forward field, measurements of discharge # 27100 (figure 1, table 1) are shown. The absolute values presented here are only valid for this specific discharge. The qualitative trends of the various parameters during the three detachment states are, however, valid for all discharges made in forward field with deuterium. Figure 4 shows the calculated DOD of the inner and outer divertor as a function of the line-integrated edge plasma density. To determine the two constants C in equation (6) for the inner and outer divertor, the mean values of meas D + (1.8 s < t < 1.9 s) before the fuelling ramp are set equal to calc D + . At this time the inner divertor is already in a high recycling regime although this is the lowest achievable main plasma density in these density ramp discharges. The measured and calculated temporal evolutions of D + to the inner and outer divertor are shown in figures 5(a) and (b). From this, the onsets of detachment (when meas D + rolls over) of the inner and outer divertor are set ton e ≈ 1.5 × 10 19 m −2 (t ≈ 2 s) and n e ≈ 3.3 × 10 19 m −2 (t ≈ 2.85 s), respectively. Before the onset of the inner divertor detachment at t < 2 s, D + to the inner divertor is higher than that to the outer divertor. The 3 is more symmetric than the total ion flux ratio of in D + / out D + = 1.9. This means that the inner ion flux profile is broader than the outer one, which indicates that the inner divertor is already in a higher recycling regime, as mentioned above. Before the onset of detachment (t < 2 s) the electron density in the divertor volume is below the measurement range of n e > 4 × 10 19 m −3 of the SBD in both the inner and outer divertor. This is expected as the density at the targets, measured by probes, is below 1.5×10 19 m −3 , which corresponds to a density at the recycling zone of n e,V ≈ 2 · n e,t ≈ 3 × 10 19 m −3 (e.g. [30]).
3.1.1. The onset of detachment state. The start of this state is defined by the first deviation from the TPM scaling, which occurs in the inner divertor atn e ≈ 1.5×10 19 m −2 (figure 4(a)) or at t ≈ 2 s (figure 5(a)). Namely, meas D + becomes less than the TPM scaling and the DOD exceeds unity.
Inner divertor. During this state, the ion flux close to the inner strike point, S ≈ 1 cm rolls over and drops to D + ≈ 1 × 10 22 m −2 s −1 with increasing upstream density (figure 6(h)). This is also visible in the total ion flux to the inner divertor, which further deviates from the TPM scaling (figure 5(a)) and the DOD increases (figure 4(a)). Also n e,t close to the strike point decreases with increasing upstream density, but, in contrast, increases in the far SOL at S ≈ 14 cm up to n e,t ≈ 2.3 × 10 19 m −3 at the end of the OS (figure 6(d)). This is consistent with the radiation distribution measured by foil bolometry, shown in figure 7. The radiation is higher in the inner far SOL than close to the strike point. In addition, the electron density in the volume increases up to n e,V ≈ 2.3 × 10 20 m −3 (figure 6(b)). All in all, this indicates that the plasma is partially detached from the inner strike point region at the end of this state.
Outer divertor. The outer divertor is still attached, in the conduction limited regime and follows the simple TPM (DOD = 1) throughout this state (figures 4(b) and 5(b)). With increasing upstream density, the maximum of D + and n e,t increases during this state up to 4 × 10 22 m −2 s −1 and 1.4 × 10 19 m −3 , respectively, while T e,t drops to 25 eV (figures 6(i), (g) and (e)). The electron density in the volume stays below 4 × 10 19 m −3 (figure 6(c)).
3.1.2. The fluctuating detachment state. This state is defined by the appearance of radiative fluctuations, which are situated close to the X-point in the inner SOL. During this state, the core plasma fuelling becomes less efficient. Although the amount of the fuelling gas is steadily increased, the core plasma density seems to saturate (figure 1(c), t ≈ 2.9 s). The characteristics of these fluctuations and the evolution of the divertor plasma parameters during this state are described in the following.
The X-point fluctuations. The transition to this state is determined with a sudden onset of a fluctuation band of f ≈ 5.5 kHz (figures 5(c) and (d)), measured with the AXUV diodes, which is observed for the first time. The spectrogram was derived with a short-time Fourier transform with a sample window size of n FFT = 4096 (the choice of n FFT was found to have no significant impact on the power spectra). The width of this fluctuation band is f ≈ 3 kHz. Figure 8 shows a zoom of an AXUV time trace measured with the orange chord in figure 2(b). The mean value of the radiated power is ≈2.5 MW m −2 and its standard deviation is There is currently no other diagnostic available measuring with such a high sampling rate in the corresponding region in order to trace these fluctuations back to the electron temperature or to the density or to a combination of both. Figure 9 shows the average frequency power spectra of the fluctuations for various diodes. First the spectrogram was made as described above and then averaged over the time interval from 2.4 to 2.6 s. The width and the mean frequency are indicated for a specific diode. With all AXUV channels the position of these fluctuations can be located. The strength of the fluctuations is derived by integrating over the spectrum after subtracting the background level. The background is due to electronic noise, which is at these rather low frequencies determined by flicker noise and can thus be approximated with an exponential function. The fit of an exponential function on the spectrum is also shown in figure 9. The exponential function is a sufficient assumption for the background as we are interested in the relative strength of the various signals and not in absolute numbers. The resulting fluctuation strength for all diodes is shown in figure 10, where the colour code represents the strength. It can be seen that the radiative fluctuations are located close to the X-point in the inner SOL.
Inner divertor. At the start of the FS, there is a sudden increase in D + (figure 5(a)) and D + as well as an abrupt shift of the peak D + position away from the strike point from S ≈ 1 cm to S ≈ 3 cm (figure 6(h)). During this state, the ion flux at this position first increases up to D + ≈ 3.2 × 10 22 m −2 s −1 and then rolls over at t ≈ 2.6 s. The target electron density at the strike point region shows the same shift and also rolls over, see figure 6(d). In contrast, the electron temperature at this narrow region ( S ≈ 3 cm) steadily increases up to about T e,t ≈ 36 eV (figure 6(f )) while the pressure there remains almost constant. The ion flux in the far SOL at S > 14 cm increases throughout this state, whereas n e,t in this region, which is higher than at the strike point, rolls over during this state. The temperature in this region remains low, T e,t ≈ 4 eV.
At the transition to the FS the peak density in the volume, n e,V , shifts from S ≈ 10 cm to S ≈ 4 cm (figure 6(b)). Associated with the second rollover of D + and n e,t at the strike point region (figures 6(h) and (d)) a region of high density ≈2.5 × 10 20 m −3 develops in the volume of the inner far SOL ( S ≈ 15 cm, figure 6(b)). This density is an order of magnitude higher than n e,t andn e . In the following, these regions are called high density fronts. The position can be verified with the vertical n e,V measurements (figure 6(a), R = −14 cm), which are from the leftmost LOS (figure 2(a)) close to the target. In addition, a second high density front starts to develop in the inner SOL close to the X-point (figure 6(a), R = −2 cm). The region where the SBD diagnostic measures the density corresponds to regions where the radiation is the highest (P rad ∝ n 2 e ). Therefore, the total radiation distribution measured by foil bolometry can be used as an approximation of the density distribution. The radiation distribution for t = 2.9 s is shown in figure 11 and the approximated positions of the high density fronts are indicated. It is also possible, according to the radiation measurement, that this is just one density front rather than two. In any case, however, the density front in the inner divertor expands into the inner far SOL at S ≈ 15 cm, consistent with the increase in the ion flux and target electron density in this region. With increasing upstream density, first the spatial extent of the X-point high density front grows into the inner SOL and n e,V rises up to ≈2.5 × 10 20 m −3 and then rolls over (figure 6(a)).
Outer divertor. During the FS the ion flux and the electron density at the outer target first increase and then roll over as in the inner one (figures 6(e) and (i)). The peak positions of D + and n e,t remain constant during the discharge. Moreover, meas D + starts to surpass the TPM scaling, meas D + > calc D + ( figure 5(b)), which in the following will be called flux enhancement. Consequently, the DOD drops below 1, see figure 4(b). Contrary to the inner target, T e,t also increases while D + and n e,t increase and then rolls over ( figure 6(g)). This simultaneous increase in T e,t and n e,t leads to a rise in the outer divertor pressure by ≈100%.
In line with this, the density in the outer divertor volume close to the strike point rises by more than an order of magnitude up to n e,V ≈ 4 × 10 20 m −3 (figure 6(c)), reaching  its maximum after D + and n e,t rolled over. As the spatial extent of the Stark diagnostic in the outer divertor is limited to S < 15 cm (figure 2(a)) it cannot be verified if there exists a high density front in the far outer SOL or X-point region similar to the one in the inner divertor.
3.1.3. The complete detachment state. The beginning of this state is defined when the X-point fluctuations disappear ( figure 5(d)). With the transition from the FS to the CDS, the core plasma fuelling becomes more efficient again. This can be seen in the time traces of the line-integrated plasma density and the applied fuelling gas puff ( figure 1(c), t ≈ 3 s). The plasma density increases faster at this point while the fuelling rate remains constant. In the following, the evolution of the divertor plasma parameters are described in detail and the occurrence of volume recombination will be discussed.
Inner divertor. With the start of this state n e,t , T e,t and D + at the strike point region are reduced by more than an order of magnitude (figures 6(d), (f ) and (h)). Also the high density front at the strike point region disappears and moves along the field lines towards and even above the X-point. With the horizontal and vertical n e,V measurements, the motion of the high density front can be monitored. At the beginning, the density front is located at S = 15 cm ( figure 6(b)) and close to the target at R = −14 cm ( figure 6(a)). Then the front moves in horizontal as well as in vertical direction until it is close to the X-point at R = −2 cm and S = 38 cm (which are the uppermost horizontal LOS, figure 2(a), being above the X-point). The final position of the density front, at t = 3.5 s, is consistent with the radiation distribution (figure 12), which peaks well above the X-point. We call here the situation when the target values n e,t , T e,t and D + and also the electron density in the volume, n e,V , almost vanish at the strike point region complete detachment 2 . Thus, the name for this third detachment state. It should be noted here, that there is a short increase in T e,t close to the strike point just after the beginning of this state when the density front starts to move towards the X-point (t ≈ 3 s, figure 6(f )). The uncertainty in the determination of the strike point position is ≈1 cm. It is therefore not possible to clarify if this short increase in T e,t occurs in the SOL or in the private flux region. It is also unlikely to be a measurement error of the LPs as this feature is observed in every discharge of this density ramp series.
Outer divertor. At the transition from the FS to the CDS, D + in the outer divertor becomes smaller than the TPM scaling and the DOD exceeds unity (figures 5(b) and 4(b)). At this point, D + at the outer target is already strongly reduced by two orders of magnitude with respect to its maximum value (figure 6(i)). Also the density and the temperature at the target close to the strike point region ( S < 5 cm) have reached low values of n e,t 2 × 10 19 m −3 and T e,t 5 eV. Moreover, the high density front in the outer strike point region rapidly moves out of the spectroscopic observation area ( S < 15 cm) at the beginning of this state (figure 6(c)). In the observed region the plasma is therefore completely detached from the outer target, confirmed by the measurement of the total radiation (figure 12), which peaks close to the X-point. It is remarkable that the complete detachment starts simultaneously at the inner and outer strike point regions. This has not yet been observed elsewhere.
Evidence for volume recombination and low divertor temperatures. The density in the divertor volume, the emissivity of D δ and the line ratio D δ /D are shown in figure 13. First it can be seen that the D δ emission increases when the density has decreased, in the inner as well as in the outer divertor. In other words, when the density front has moved towards the X-point (above the blue dashed line in figure 13(a)), the line emission increases between the density front and the target (below the blue dashed line in figure 13(c)). The TEC, shown in figure 3(c), increases with decreasing temperature and reaches its maximum at T e ≈ 1.5 eV. This peak corresponds to the transition from an ionization to a recombination dominated plasma (section 2.3) and the temperature is approximately ≈1.5 eV. Thereafter, when the emission decreases, the line ratio of D δ /D starts to increase (below the red dashed line in figures 13(c)-(f )). From figure 3(d) it can be seen that the line ratio increases when recombination becomes dominant and the temperature is below 1 eV. This is consistent with the drop in the TEC below T e = 1 eV (figure 3(c)). As these are line-integrated measurements, we do not aim at deducing absolute temperatures out of the D δ /D ratio. However, we can  assume that the radiation of D δ and D is emitted from the same region and draw qualitative conclusions. Namely that, in the inner and outer divertor volume, recombination becomes dominant and the electron temperature is T e < 1 eV at times and regions below the red dashed lines in figure 13.

Detachment in hydrogen
To disentangle isotope effects, several discharges of the density ramp series were performed with hydrogen as main ion species (see table 1). The divertor plasma undergoes the same three detachment states in hydrogen as in deuterium. The characteristics of the different detachment states described above qualitatively hold also for a hydrogen plasma with the following main quantitative differences. The ratio of the total ion flux to the inner and outer divertor before the beginning of the fuelling ramp (t < 1.9 s) is in D + / out D + = 1.6 (figures 14(a) and (b)), which is more symmetric compared with the deuterium-fuelled case ( in D + / out D + = 1.9). In addition, the radiative X-point fluctuations during the fluctuating detachment state have a frequency of f ≈ 8 kHz in

The three detachment states in reversed field
In this section we describe the evolution of the divertor plasma when B t and I p are reversed and compare it with the forward field case. Representative for all discharges of the series, which are made in reversed field, we show measurements of discharge # 27284 (table 1). Discharge # 27101 in forward field has the same heating power as this discharge # 27284 in reversed field. But in discharge # 27101 we observed divertor plasma oscillations [34], thus we do not compare this pair of discharges here. When these discharges were carried out, foil bolometry was not available. Therefore, no measurements of the radiation distribution in the divertor can be shown here. As in forward field, there are three different states during the evolution of detachment. The qualitative development of the target parameters n e,t , T e,t and D + in the inner, respectively, outer target in reversed field is rather comparable to the outer, respectively, the inner target in forward field. Whereas the density in the divertor volume evolves quite similar in both field directions. Figure 15 shows the DOD as a function of the lineintegrated edge plasma density of the inner and outer divertor and the corresponding measured and calculated temporal evolutions of D + are shown in figure 16. The onsets of detachment (rollover of D + ) of the inner and outer divertor are therefore at t ≈ 2.4 s (n e ≈ 2.1 × 10 19 m −2 ) and t ≈ 2.5 s (n e ≈ 2.5 × 10 19 m −2 ), respectively. Before the start of the fuelling ramp, t < 1.9 s, the total ion flux to the outer target is larger than that to the inner target, out D + / in D + = 3.6 (figures 16(a) and (c)). This ratio is less symmetric compared with the forward field case and, contrary to forward field, in favour of the outer divertor. Figure 17 shows the inner and outer target profiles of n e,t , T e,t and D + as well as the density measurements in the inner and outer divertor volume. Before the start of the fuelling ramp, peak ion fluxes of D + ≈ 8 × 10 21 m −2 s −1 and D + ≈ 5.2 × 10 22 m −2 s −1 close to the inner and outer strike points are measured, respectively.

The onset of detachment state.
As in forward field, the start of the OS is defined by the first deviation from the TPM scaling. This happens, similar to forward field, in the inner divertor. Contrary to forward field, the X-point fluctuations appear already in this state. Their amplitude grows during this state until, at the end of this state, its maximum is reached.
Inner divertor. Contrary to forward field, the measured total ion flux increases more strongly compared with the TPM scaling ( figure 16(a)). Thus, the flux enhancement occurs now in the inner divertor and the DOD falls below unity ( figure 15(a)). During this state D + and n e,t increase up to D + ≈ 5×10 22 m −2 s −1 and n e,t ≈ 6×10 19 m −3 , respectively, and then roll over. The target temperature first decreases with increasing n e,t and D + and increases when n e,t and D + roll over (figures 17(d), (f ) and (h)). Associated with the rollover, a high density front of n e,V ≈ 2 × 10 20 m −3 develops in the SOL at S ≈ 7 cm, see figure 17(b). It should be noted that, while D + increases between t = 2.1 s and t = 2.3 s, there seems to be a shift of D + back to S ≈ 3 cm at t = 2.2 s ( figure 17(h)). But it is more likely that the peak of the ion flux profile moves between two probe positions in this case.
Outer divertor. The measured D + follows the TPM scaling throughout this state and the DOD is 1, see figures 15(b) and 16(b). The peak position of D + and n e,t remains constant during the discharge (figure 17(e) and (i)). D + rises up to ≈1.6 × 10 23 m −2 s −1 and n e,t up to ≈5 × 10 19 m −3 . Similar to the inner divertor in forward field, the electron temperature at the target increases with increasing D + and n e,t throughout this state ( figure 17(g)). The density in the volume close to the strike point increases up to ≈1.5 × 10 20 m −3 , see figure 17(c).

The fluctuating detachment state.
In reversed field, the start of this state is defined when the strength of the X-point fluctuations reaches its maximum, see figure 16(d).
The X-point fluctuations. Contrary to forward field, two frequency bands, one at f ≈ 4.5 kHz and one at f ≈ 9 kHz are observed ( figure 16(d)). The width of each of these frequency bands is f ≈ 3 kHz, which is similar to forward field.
The maximum of the fluctuations is still located in the inner SOL close to the X-point, see figure 18. Their spatial extent, however, is larger than that in forward field and seems to expand into the outer divertor SOL.
Inner divertor. During this state, the ion flux and the target density steadily drop further to D + ≈ 5 × 10 21 m −2 s −1 and n e,t ≈ 7 × 10 18 m −3 , respectively (figures 17(d) and (h)). Furthermore, the profile of n e,t gets broader. The target temperature first increases further up to T e,t ≈ 13 eV and then rolls over within this state ( figure 17(f )). Associated with the further decrease in D + and n e,t , the high density front at the strike point region ( S < 10 cm) rises up to n e,V ≈ 3.7 × 10 20 m −3 and then rolls over when T e,t rolls over ( figure 17(b)). Linked to the fluctuations high density fronts of n e ≈ 3 × 10 20 m −3 (figures 17(a) and (b)) develop in the inner far SOL ( S ≈ 15 cm) and X-point region ( R ≈ −2 cm). This is similar to forward field. Contrary to forward field, the X-point high density front reaches its maximum at the end of the FS.
Outer divertor. D + , D + and n e,t roll over at the start of this state (figures 16(b) and 17(e) and (i)) and the DOD exceeds unity ( figure 15(b)). The target temperature steadily increases throughout this state up to T e,t ≈ 50 eV ( figure 17(g)). Furthermore, T e,t strongly fluctuates, which is most likely linked to the radiative X-point fluctuations. As the time resolution of the LPs is too slow, a correlation analysis with the AXUV diodes can not, however, be made. Associated with the further decrease in D + and n e,t , the high density front at the strike point region increases up to n e ≈ 3 × 10 20 m −3 during this state ( figure 17(c)).

The complete detachment state.
The beginning of the CDS is defined, similar to forward field, when the radiative X-point fluctuations vanish. The finally achieved DOD is ≈40 and ≈9 for the inner and outer divertor, respectively (figure 15). Compared with the forward field case, this is much lower (inner DOD ≈ 600, outer DOD ≈ 12) but again higher in the inner divertor.
Inner divertor. At the start of this state, the target parameters at the strike point region ( S < 10 cm) have already reached very low values of D + < 2×10 21 m −2 s −1 , n e,t < 3×10 18 m −3 and T e,t < 2 eV (figures 17(d), (f ) and (h)). Also the high density front in this region has vanished ( figure 17(b)) which, according to our definition, indicates that the plasma is completely detached from the inner strike point region. Moreover, similar to forward field, the high density front from the inner strike point region moves upwards along the field lines well above the X-point (figures 17(a) and (b)).
Outer divertor. The ion flux and the density at the target drop further during this state (figures 17(e) and (i)). Similar to the inner divertor in forward field, the electron temperature at the strike point region ( S ≈ 5 cm) starts to decrease (here to T e,t ≈ 6 eV at the end of the discharge) while there is a short strong increase in T e,t in the private flux region ( figure 17(g)).
The high density front in the strike point region ( S < 10 cm, figure 17(c)) is reduced by ≈50% to n e ≈ 1.5 × 10 20 m −3 during this state. The position of the peak n e,V moves slightly upstream, but, contrary to forward field, stays in the target region ( S < 10 cm) until almost the end of the discharge.

Evidence for volume recombination and low divertor tempera-
tures. Similar to forward field, there is evidence for volume recombination and thus electron temperatures below ≈1 eV in the inner and outer divertor. Figure 19 shows the density in the divertor volume, the emissivity of D δ and the line ratio D δ /D . It can be seen again that the line emission increases when the high density front has moved away from the target (below the blue dashed line in figures 19(a) and (c)), indicating temperatures of ≈1.5 eV when the emission reaches its maximum. When the line emission decreases, the D δ /D line ratio increases, and electron temperatures below ≈1 eV can be expected at times and regions below the red dashed lines in figure 19.

Effect of MPs
When these experiments were carried out, ASDEX Upgrade was equipped with eight in-vessel saddle coils [35] in order to externally produce MPs. They are located at the low-field side, four coils are mounted above and four coils are mounted below the midplane. The discharge #27101 was repeated with the coils switched on (table 1). The MP field produced by the coils has a toroidal mode number of n = 2 and the currents of the upper and lower coils, I coil = 1 kA, are applied with odd parity. Figure 20 shows D + and the power spectrum of an AXUV diode of discharge # 27101 (without MP) in comparison with discharge # 27102 (with MP). Before the onset of detachment, the total ion flux to the inner target is 2 × 10 22 s −1 with and without MP. With MP D + in the outer divertor is slightly higher ( D + = 1.  which are discussed in [34] and are not of importance for this comparison. The main difference in the evolution of divertor detachment with and without MP begins when the outer divertor starts to detach, i.e. when the outer D + rolls over. With MP the outer D + then drops abruptly (figure 20(d)) and the X-point fluctuations vanish (figure 20(h)), which determines the end of the FS. In the case without MP, there is a smooth rollover of the outer D + (figure 20(c)) and the end of the FS (figure 20(g)) happens later than in the MP case.
The CDS with MP can be divided into two parts. At the beginning of the CDS the high density fronts in the inner far SOL and X-point region disappear (figures 21(b) and (d)) as abruptly as the drop in the ion flux to the outer target. At the same time there is a sharp strong increase in the main plasma density (see calc D + in figure 20(d) which is proportional to the main plasma density). The plasma is completely detached from the inner strike point region ( D + ( S < 8 cm) < 1 × 10 21 m −2 s −1 ) at the beginning of the CDS, but the peak D + in the far SOL shifts towards the strike point ( figure 21(h)). The peak D + at the outer strike point drops at the beginning of the CDS to D + ≈ 6.9×10 22 m −2 s −1 , which is comparable to the case without MP (figures 21(i) and (j )). The high density front in the outer divertor moves upstream ( S = 2 cm to S = 5 cm) and, contrary to the case without MP, stays in this region (compare figures 21(e) and (f ), 3.2 s). During the second part of the CDS with MP this outer high density front moves out of the region covered by the Stark diagnostic. The DOD with and without MP is shown in figure 22. It can be seen that the CDS starts slightly earlier with MP (n e = 3.2 × 10 19 m −2 without MP andn e = 3.8 × 10 19 m −2 with MP). Furthermore, with MP detachment in the inner and outer divertor proceeds faster with respect to the upstream density. Consequently, the density limit occurs earlier with MP, i.e. atn e = 4.6 × 10 19 m −2 compared withn e = 5 × 10 19 m −2 without MP.

Discussion
Role of E × B drifts. It was proposed in [15] that plasma flows induced by a combination of radial and poloidal E × B drifts, which change direction when the field is changed [36], drive asymmetries of the ion flux reaching the inner and outer divertor. Due to the variation of the pre-sheath potential drop a poloidal electric field E is formed in front of the target. The resulting E ×B drift induces a radial flow dr r . In forward field this flow is directed from the outer SOL across the separatrix into the private flux region (PF) and from the PF into the inner SOL. In addition, a radial electric field E r in the PF results in a poloidal flow dr induced by the E r × B drift. This flow in the PF is in forward field directed from the outer to the inner divertor. For similar conditions, such a flow in the PF has been measured in JT-60U [37] and ASDEX Upgrade [38]. Thus, the combination of both, the dr flow in the PF and the dr r flow, brings more plasma to the inner divertor in forward field and to the outer divertor in reversed field. It was further shown at ASDEX Upgrade that the E × B drifts have to be taken into account in order to simulate low-density attached divertor plasmas correctly [39].
Such an asymmetry was also observed here. At the lowest density before the fuelling ramp starts, the ratio of the total ion flux reaching the inner and outer divertor in forward field is asymmetric and in favour of the inner divertor ( in D + / out D + = 1.9). In reversed field, this ratio is still asymmetric but now being in favour of the outer divertor ( in D + / out D + = 0.3). It was proposed, however, that the influence of these E × B drifts becomes less important at high densities due to the flatter temperature gradients [36]. In fact, when the density is increased here, the rollover of D + happens first in the inner divertor for both field directions. The ratio of the edge lineintegrated plasma density at the inner and outer rollovers is, in reversed field,n e,in /n e,out ≈ 2.1/2.5 = 0.84. In forward field, this ratio isn e,in /n e,out ≈ 1.5/3.3 = 0.76. Taking the second rollover (see the next point) in forward field, the ratio is n e,in /n e,out ≈ 2.9/3.3 = 0.88, which is even more comparable to the reversed field case. In addition, the finally achieved DOD is, for both field directions, larger in the inner divertor. Also the X-point fluctuations and the associated high density front in the far SOL occur for both field directions in the inner divertor. This shows that the E × B drifts contribute at a low density but they have a minor influence on the overall detachment process.
Plasma evolution during the fluctuating detachment state. At the beginning of the fluctuating detachment state the total ion flux, D + , to the inner divertor and D + and n e,t close to the inner strike point suddenly increase. In addition, there is a jump of the peak D + and n e,t positions in the strike point region from S ≈ 1 cm to S ≈ 3 cm at the transition to this state. With increasing upstream density, D + and n e,t at the strike point region ( S ≈ 3 cm) roll over the second time (which will be discussed later). After their rollover, T e,t increases in this narrow region at S ≈ 3 cm while the pressure remains approximately constant. CX collisions are thus most likely not the cause of the ion flux reduction in the S ≈ 3 cm region (via f mom > 0 in equation (5)). Moreover, they are only effective at temperatures below ≈5 eV [8], which is not the case in this region. An increase in the power being convected (f conv > 0) leads also to a reduction in D + (equation (5)) and n e,t (equation (4)) and to an increase in T e,t (equation (3)), being in agreement with the measured evolution. Such a change in the ratio of conducted and convected power has been measured in the outer divertor of DIII-D [40]. Furthermore, in order to increase the fraction of convected power, the ionization front must move or expand into the SOL, which is consistent with the measured high density front in the inner divertor volume. The position and spatial extent of this high density front can be correlated with the total radiation distribution in the divertor (red circle in figure 23(a)) as recombination processes can be neglected at this point.
At the end of the FS, the fuelling of the main plasma becomes less efficient, i.e. although the fuelling puff is constantly increased, the main plasma density almost saturates. Based on Krasheninnikov's stability theory of detached plasmas [41], the main plasma density cannot be increased further by gas puffing at a certain point. Then, the cold and dense plasma buffer, which is situated between the recombination and ionization fronts, must increase and move towards the X-point. In fact, a decrease in n e,V at the inner strike point region and an increase in n e,V in the inner far SOL and X-point region are measured during the phase in which the main plasma density increases less strongly than the fuelling puff (compare also figures 23(a) and (b)).
The two rollovers in forward field. In forward field, two rollovers of D + are observed in the inner divertor strike point region, one at the OS ( S ≈ 1 cm) and one during the fluctuating detachment state ( S ≈ 3 cm) while there is no second rollover in the outer divertor, neither in forward nor in reversed field.
A possible reason for the early first rollover followed by a second rollover in the inner divertor in forward field could be a geometric effect of the divertor structure. The lower tile of the inner divertor target is tilted towards the separatrix, i.e. the angle between the target normal and the horizontal axis is negative (white arrow in figure 24(a)). During the OS the ion flux profile is radially not very broad, which is supported by the total radiation distribution ( figure 24(a)). Neutrals are   recycled from the lower inner target and released in a cos 2 distribution cone around the target normal, hence back to the strike point region (white arrow in figure 24(a)). This would enhance the neutral pressure in the inner strike point region, which increases the probability for CX collisions to remove momentum, thus the ion flux decreases if not compensated by an increase in the power loss (equation (5)). This increase in the ion flux was observed. At the transition to the FS, a mechanism sets in which brings more particles to the far SOL, i.e. to the upper tile of the inner target ( figure 24(b)). Once the ion fluxes to this upper tile are strong, and therefore recycling from this tile becomes strong, the situation should change. The upper tile curves backwards, i.e. the angle between the target normal and the horizontal axis becomes positive. When recycling takes place at this upper tile (high ion fluxes are measured in this region during the FS, confirmed by the radiation distribution, figure 24(b)), neutrals will be released into regions further upstream (white arrows in figure 24(b)). This should change the divertor plasma conditions and could be the reason for the second increase and rollover of the ion flux in the inner divertor. In order to verify this theory, similar discharges can be made with different strike point positions. With a lower strike point, a higher density should be required to push the ion flux to the upper tile of the inner divertor.
The outer target, however, is constantly tilted such that the recycled neutrals will be released back to the separatrix leg. In reversed field, D + in the outer divertor 3 scales longer with the TPM compared with forward field, then rolls over and decreases continuously. No second rollover is observed, which is consistent with this divertor geometry model. Flux enhancement. The flux enhancement, which is defined here when the total ion flux exceeds the TPM scaling, occurs in the outer divertor in forward field and in the inner divertor in reversed field. In forward field 4 , during the FS a high electron density is measured in the inner far SOL and Xpoint region, while the density in the strike point region is reduced (see the radiation distribution, figure 24(b), as an indication). Namely, the inner divertor strike point region becomes transparent for neutrals (blue arrows in figure 24(b)). Recycled neutrals, originating from the strike point region, could therefore pass the inner SOL and the private flux region and reach the outer SOL. It has been shown previously at ASDEX Upgrade [42] that, under similar conditions, the inner divertor becomes transparent for neutrals and the neutral fluxes measured in the inner divertor and private flux region are equal. These neutrals, which reach the outer divertor SOL, will ionize there. This leads to additional radiation losses (f pow > 0) in the outer SOL. As a consequence, the ion flux at the target increases (equation (5)), consistent with the observations. In addition, these ionized neutrals should provide an additional particle source in the outer SOL, resulting in a fraction of power being convected (f conv > 0). This may explain the increase in the outer target temperature (equation (3)) during the flux enhancement phase, while the target ion flux and density also increase. In total, this would then be a combination, or competition, of the f pow > 0 and f conv > 0 effects. The flux enhancement might be similar to the death rays observed in Alcator C-Mod [13] where the plasma pressure at the target sometimes exceeds the upstream values prior to detachment. But this effect was localized in the narrow region close to the strike point while the flux enhancement, observed here, occurs over a large target area and during the detachment process in every discharge.
Radiative X-point fluctuations. Once the X-point fluctuations are triggered, a high electron density and Balmer radiance is always measured at the X-point region. This indicates that the ionization front expands up the X-point, which may cause this phenomenon, pointing towards a MARFE-like instability. The frequency of the fluctuations depends inversely on the square root of the mass of the fuelling species. It was further shown in [34] that the injection of additional nitrogen also decreases the frequency. This points in the same direction, as with nitrogen the effective charge of the plasma, Z eff , is increased.
This mass dependence on the frequency suggests that the ion sound speed, c s = √ k B (T e + T i )/m i , is somehow involved. For example, ions/filaments, originating at the X-point due to the ionization of recycled neutrals (MARFE like), flow with c s from the X-point to the inner or outer target. This would be consistent with the increased fraction of convected power (f conv > 0) in the S ≈ 3 cm region of the inner divertor, as discussed above. An assumption of T i = T e = 15 eV, which is reasonable for ionizing conditions, gives c s ≈ 38 km s −1 . The connection length from the inner X-point, starting at a horizontal distance from the X-point which corresponds to S ≈ 3 cm at the target (≈7 cm in real space or ρ pol ≈ 1.004 in normalized flux) towards the outer divertor is L c ≈ 62 m. This yields a characteristic frequency of f ≈ 0.6 kHz which is too low. The connection length to the inner divertor, L c ≈ 6.4 m, gives a frequency of f ≈ 5.9 kHz. This is a reasonable agreement, despite the uncertainty in the calculation of c s and L c . The underlying physical mechanism, however, cannot be explained here. As a first step, an additional perpendicular transport in the inner X-point region was incorporated into numerical simulations [43]. It should also be mentioned that this instability may also be a kind of limit cycle. The ionization front close to X-point leads to an instability which transports the plasma away, e.g. in the far SOL. The inner divertor is then shortly re-attached and starts to detach again. It cannot be verified, however, whether the density oscillates with the frequency of the fluctuations between the high density front at the X-point and the far SOL or strike point region, as the time resolution of the SBD and the LPs is too low. New and faster diagnostics are therefore needed to gain more information on this topic.

Summary and conclusion
The objective of this paper was to present an experimental investigation of the evolution of divertor detachment at ASDEX Upgrade (AUG). With new diagnostics a better knowledge of the plasma parameters, especially of the electron density in the divertor volume, was obtained, resulting in a consistent picture of the detachment process.
The main result of this work is a new classification of divertor detachment. The detachment process is not continuously evolving but undergoes three different states where the inner and outer divertor plasma conditions are strongly coupled. It starts with the onset state, when the first deviation of the target ion flux from the simple two-point model (TPM) occurs. This happens in the inner divertor with the rollover of the ion flux (DOD > 1) close to the strike point, while the outer divertor remains attached during this state (DOD = 1).
The appearance of radiative fluctuations, which are observed for the first time, characterizes the start of the fluctuating detachment state. These fluctuations have a mean  frequency of f ≈ 5.5 kHz, a width of f ≈ 3 kHz and are situated in the inner SOL close to the X-point. From deuterium to hydrogen, the mean frequency is increased by the square root of the mass ratio of both species, i.e. f ≈ 8 kHz. In addition, regions of densities, one order of magnitude higher than the main plasma density, develop in the inner far SOL and X-point regions. The outer divertor is still attached during this state, but the ion flux exceeds the TPM scaling (DOD < 1). This so-called flux enhancement is most likely caused by an enhanced ionization of recycled neutrals originating from the inner divertor. As the inner divertor is already partially detached, it becomes transparent for recycled neutrals, which can now reach the outer SOL where they are ionized. The inner divertor plasma thus influences the outer one and encourages the outer divertor detachment. In conclusion, in order to be able to model the outer divertor detachment at AUG correctly, one must be able to reproduce the detached plasma conditions in the inner divertor together with the X-point fluctuations.
The transition to the complete detachment state happens when the radiative X-point fluctuations vanish. At this point the inner and outer divertor simultaneously start to detach completely from the strike point regions. The complete detachment is defined here when the target parameters D + , n e,t and T e,t drop to significantly lower values and, the main point, when the high density fronts in the strike point regions vanish. During the complete detachment state, the high density fronts move from the targets towards and even above the X-point, resulting in a MARFE and a density limit disruption. It was shown by means of spectroscopy, that, once the high density fronts have moved away from the targets, recombination is dominant and temperatures are below ≈1 eV only during this state and in the regions between the high density fronts and the targets.
The three detachment states are observed in reversed field, too. The radiative X-point fluctuations now consist of two frequency bands of f ≈ 4.5 kHz and f ≈ 9 kHz, but they are again located in the inner SOL close to the X-point. Moreover, the E × B drifts were found to contribute at a low density but they have a minor influence on the overall detachment process.
Finally, the effect of an additional magnetic perturbation field (MP) on the detachment process was studied. Detachment proceeds similarly with and without MP until the ion flux to the outer divertor rolls over. With MP, this rollover is followed by an abrupt and strong drop in the ion flux in the outer divertor and the electron density in the inner far SOL and X-point region, associated with an abrupt strong increase in the main plasma density. Moreover, detachment starts slightly earlier and proceeds faster with MP.