Acción de acceso a la información pública

Electron cyclotron emission (ECE)

The electron cyclotron emission (ECE) of the plasma gives information on the electron tem- perature𝑇𝑒. The electrons emit radiation at the angular electron cyclotron frequency𝜔𝑐,𝑒=_𝑚𝑒𝐵_𝑒 and its harmonics 𝜔𝑘 = 𝑘 𝜔𝑐,𝑒 while gyrating around the magnetic field lines. In optically thick plasmas, i.e. assuming that 𝑇𝑒 is equal to the radiation temperature at the cold reso- nance position of the measured frequency, the intensity at the cyclotron frequency equals the Planck curve. Due to the Maxwellian velocity distribution of the electrons and when the mea- sured plasma element is optically thick, Planck’s law of black-body radiation holds. For high temperatures, this results in the classically derived Rayleigh-Jeans expression:

𝐼𝜔 =

𝜔2

3.1 Measurements of plasma parameters 27

where𝐼𝜔 is the spectral radiance at a given frequency𝜔. In optically thick plasmas the mea- sured emission region is identified with the position of cold resonance𝜔𝑐,𝑒 (neglecting rela- tivistic and Doppler effects when the ECE antenna is measuring radiation perpendicular to the magnetic field𝐵). Owing to the spatial variation of𝐵in a tokamak configuration (𝐵 _∝1/𝑅), the location of the emission can be identified. Thus, by measuring the spectral radiance at the corresponding frequency, the electron temperature can be deduced directly via the Rayleigh- Jeans approximation. In general, the optically thick plasma approach is applied. If the plasma is optically thin the assumptions of black-body radiation and discretely localized emission are not applicable due to the shine-through effect. The shine-through peak, i.e. an increased radi- ation temperature measured around the separatrix and in the near scrape-off layer, is observed when 𝑇𝑒 exhibits a steep gradient in a low density region [88] (e.g. at the plasma edge of H-modes).

At AUG the ECE diagnostic consists of a heterodyne microwave radiometer which measures the spectral radiance at 60 different frequencies between 89 and 187 GHz [89]. The system is based on measuring the second harmonic of the ECE in the extraordinary mode (X-mode). It has a high frequency resolution (300 or 600 MHz bandwidth) and therefore, a high radial res- olution (up to 1 cm). The sampling rate of the diagnostic with the standard acquisition time is 32 kHz, thus enabling highly temporally resolved𝑇𝑒profiles to be obtained. A new acquisition system was recently installed enabling sampling rates of up to 1 MHz.

Thomson scattering (TS)

The technique of incoherent scattering of laser light is the most common diagnostic tool to measure the electron temperature (𝑇𝑒) and density (𝑛𝑒) in tokamaks. Thomson scattering (TS) is based on elastic scattering of an electromagnetic wave by a charged particle (here, free electrons). The particle gets accelerated by the electromagnetic wave and while it accelerates it emits radiation and the wave is scattered. The Doppler effect has to be taken into account for the scattered radiation since the particle moves relative to the incident wave, but also relative to the scattered wave. Hence, the scattered wave is Doppler-shifted by

Δ𝜔=v_⋅(k𝑖 −k𝑠) (3.12)

wherevis the velocity of the charged particle,k𝑖is the wave vector of the incident wave and k𝑠the wave vector of the scattered wave. In tokamaks, TS is usually performed at a scattering angle of about 90° and due to 𝑚𝑒 ≪ 𝑚𝑖 (𝑚𝑒 being the electron mass and𝑚𝑖 the ion mass) mainly electrons are accelerated and emit radiation. The Doppler width of the measured scat- tered spectrum gives information on𝑇𝑒. In addition, the intensity of the scattered radiation is proportional to𝑛𝑒, thus allowing for a simultaneous measurement of𝑇𝑒and𝑛𝑒.

At AUG edge 𝑇𝑒 and 𝑛𝑒 profiles are measured with the standard multi-pulse Nd-YAG (neodymium yttrium aluminium garnet) laser TS diagnostic, which consists of an edge and a core system [90]. The edge (core) system employs six (four) 20 Hz laser beams (with a pulse energy of about 1 J and a pulse duration of 10 ns) with a diameter of about 2 mm which are launched vertically through the plasma edge (core). The scattered light is collected through a horizontal port via 10 (16) four channel polychromators allowing simultaneous𝑛𝑒 and𝑇𝑒 measurements at the same radial position to be obtained. The spectral ranges of the four chan- nels of the polychromators are determined by interference filters which are set up in front of avalanche diodes. The spatial range of the edge TS system can be extended using the radial plasma sweep technique (see section 3.2). The repetition rate of the diagnostic is 8 ms, while

28 3. Edge diagnostics and experimental techniques at ASDEX Upgrade

the radial resolution is 3 mm for the edge system and 25 mm for the core system [90]. Com- plete, detailed radial𝑇𝑒profiles are obtained by combining the profiles measured with the TS and ECE diagnostics, provided that the toroidal magnetic field is high enough to avoid the ECE propagation cut-off at high density.

Impact excitation spectroscopy on a lithium beam

Injecting a neutral lithium (Li) beam into the plasma allows the Li0resonance line at 670.8 nm, corresponding to the transition Li0(2p_→2s) to be measured [91]. The injected Li atoms col- lide with the plasma particles and hence, the resulting emission profile is directly connected to the electron density, 𝑛𝑒. Ionization and charge exchange with the background plasma par- ticles attenuate the Li beam, which restricts the measurements to the plasma edge (typically up to𝜌𝑝𝑜𝑙 = 0.95, depending on the density). From the emission profile the electron density is calculated via a collisional-radiative model, which accounts for electron impact excitation, ionization and charge exchange.

At AUG neutral Li atoms are injected horizontally into the plasma, i.e. near the equatorial midplane of the torus, at an energy of 30 to 60 keV [92, 93]. The beam is observed with an optical head, which is equipped with 35 LOS. The emissivity of the Li0(2p_→2s) transition is measured using interference filters and photomultipliers. The background radiation from the plasma is subtracted by chopping the Li beam periodically. The modulation periods of 56 ms beam on and 24 ms beam off are used to measure the background, thus allowing an accurate background subtraction in stationary plasmas [93]. For the study of transient events such as the L-H transition or the edge localized mode (ELM) cycle the modulation frequency of the beam chopping technique can be increased to 2 kHz. The Li beam diagnostic can be operated with a temporal resolution down to 50 µs, while the radial resolution is determined by the observation volume which has an extent of 5 mm.

DCN laser interferometry

Another method to measure the𝑛𝑒profile is laser interferometry, which is based on the interac- tion of electrons with an electromagnetic wave with the additional dependence on the variation of the plasma refractive index𝑁. 𝑁 is directly connected to𝑛𝑒:

𝑁 = √ 1₋ 𝜔 2 𝑝 𝜔2 0 = √ 1₋𝑛𝑒 𝑒2 𝜖0𝑚𝑒𝜔02 (3.13) ≈ 1₋𝑛𝑒 𝑒2 2𝜖0𝑚𝑒𝜔02 (3.14) where 𝜔𝑝 is the plasma frequency, 𝑒 the elementary charge, 𝜖0 the electric constant, 𝑚𝑒 the electron mass and 𝜔0 the angular frequency of the electromagnetic wave. Using a Taylor

expansion, which holds if𝜔0 ≫𝜔𝑝, the refractive index can be simplified to equation (3.14). The phase difference Δ𝜙 is measured by comparing the propagation of an electromagnetic wave along a path through the plasma to the propagation along a path through vacuum. This phase shift is proportional to the line-integrated electron density of the plasma. Introducing the classical electron radius𝑟𝑒 =𝑒2/4𝜋𝜖0𝑚𝑒𝑐2, where𝑐is the speed of light, and the vacuum