Disruption Specification in ARIES

C. Kessel, PPPL

ARIES Project Meeting, January 23-24, 2012, UCSD

Continuing the loading description for PFCs

divertor/heat nominal nominal transient off-normal transient

PSOL(rad+cond) ELMs disruption

divertor/particle nominal nominal transient off-normal transient

DT,He,Ar ELMs disruption

FW/heat nominal nominal transient off-normal transient

Prad,core ELMs disruption CX neutrals runaway electrons stationary core MARFE fast confinement loss stationary X-pt MARFE fast alpha particles

FW/particle nominal nominal transient off-normal transient

DT flux ELMs disruption CX flux runaway electrons fast confinement loss fast alpha particles

Disruption Basics• Major concerns from disruptions

– Energy deposition on FW and divertor (melting and erosion)– Electromagnetic loads (induced eddy currents and halo currents)– Runaway electrons (local deposition of high energy e’s on FW)

• For ARIES, a major disruption (MD) and a vertical displacement event disruption (VDE) are the scenarios we will address

• Disruption phases– Predisrupt plasma stored energy loss (small for high βN plasmas), but VDEs undergo H-mode to L-mode

transition when they hit first wall– Thermal quench (fast, ~ 1 ms)

• Fast pressure drop causes a toroidal flux change leading to induced poloidal eddy currents• Fast energy pulse to divertor and FW (~ 1 ms)• VDE has plasma in contact with FW during thermal quench

– Plasma current quench ( ~ 25 ms)• Radiative energy loss to FW, 50-100% to FW, with 0-20% conducted to divertor or FW• Drop in Ip induces eddy currents in structures• Halo current develops in later ½ to 1/3 of Ip drop

– Runaway electron generation

For ARIES, vertical displacement events (VDE) and major disruptions (MD) are appropriate

VDE:1)Plasma drifts vertically2)Plasma contacts wall, has an H-L mode transition3)Plasma continues to collapse into wall, when qedge ~ 1.5, thermal quench4)Thermal quench is about 1-2 ms long, plasma loses its stored energy5)Current quench begins as the cold plasma dissipates the plasma current, radiates magnetic energy6)Halo currents are generated in the later half of Ip drop7)Runaway electrons can also be generated in the Ip drop, which changes energy flow

MD:1)Plasma has a sudden thermal quench in its normal operating position2)Thermal quench causes all stored energy to be lost in 1-2 ms3)The current quench follows this, and radiates magnetic energy4)The plasma will move radially in response to the sudden pressure drop, and drift vertically as well, contacting the inboard FW5)Halo current and runaway electrons can be generated in these disruptions

The amount of energy released in a thermal quench, is likely the same as the high performance

plasmaIt is observed in experiments that the amount of stored energy in the plasma when it undergoes a thermal quench is actually lower than its full performance state

The plasma has undergone some transitions already, before the thermal quench, which releases some of the stored energy, this goes to the divertor, but generally over a longer time-scales

HOWEVER, for us with higher performance plasmas near beta limits, and VDE’s, the entire stored energy is available

For ARIES we should assume all the stored energy will be released in the thermal quench

The range is actually 65-100%

For VDE’s the plasma loses about ½ its stored energy when it hits the FW preceding the thermal quench

Thermal quench time, roughly correlated with plasma volume

ARIES plasma volume is about 440 m3 (for R=5.5m, a=1.375 m, κ=2.15)

This gives about Δttq ~ 1.5-2.5 ms

Variations within the same device can be large

The rise phase of power to the divertor is ~ Δttq

And the decay phase is 2-4 times longer….this is just like ELMs

ARIES

Rise phase

Decay phase

The thermal quench time is not that easy to decipher due to complexity of the process

Here is the total Te drop time (open circles), and the time for the final Te drop (closed circles) for various tokamaks….we still get about 0.6-4.0 ms range

Te in plasma center

Dα light in divertor

JET results

Thermal quench and partitioning the power to PFCs

For the disruptions we are concerned with, a small fraction of the released energy finds its way to the divertor, ~ 10-50%

This infers that 50-90% of the energy goes to the first wall

This is easy to understand for a VDE which hits the first wall before disrupting….although it also appears to be the case for ITB or high beta plasmas (MHD causes contact with the wall)

It has been observed that up to 15% of the energy released can be in the form of radiation, with peaking factor of 3.5

There is a wide variation between JET (10-50%), D3D and ASDEX-U (50-100%) for the energy fraction going to the divertor

Some magnetic energy is released on low energy disruptions

Further break the energy released in the thermal quench into that during the rise phase and that in

the decay phase

Approximately 25% of plasma energy released in thermal quench reaches PFCs in Δttq

The remaining 75% reaches the PFCs over the 2-4 times Δttq time frame following the rise phase

HOWEVER, because the energy density is so high, material damage is expected, and according to the experts we must consider the whole time that the heat flux is coming in….it is the time spent at this flux that is important

Rise phase

Decay phase

The deposition footprint in the divertor expands considerably during the thermal quench

TEXTOR is a limiter device

The deposition footprint during a thermal quench in the divertor is found to be about 5-10 times the normal steady power footprint

Recall ELMs might not show any expansion

The diverted plasmas show this trend, which does not appear as strong for limiter devices

Toroidal peaking may be up to 2 for the divertor

Try some numbers for the thermal quenchPlasma stored energy is ~ 510 MJ (for the VDE, this would about ½ this value)

Assume 10-50% to divertor, 51-255 MJAssume 50-90% to FW, 255-460 MJ, outboard onlyAssume 0-15% radiated to FW, 0-76.5 MJ, take 20% to inboard, 80% outboard

Divertor intercepting area = 1.44 x 5-10 = 7.2-14.4 m2

FW intercepting area cond/conv (outboard only) = 287 m2 / 2 (peaking) = 144 m2

FW intercepting area for radiation = 157/3.5 (peaking) inboard, 287/3.5 (peaking) outboard = 44.9 m2 (IB) and 82 m2 (OB)

Since the fluxes are so high as to damage the materials, the time over which they are above the damage thresholds is most important, so the whole pulse time will be used, ΔtTQ

dis = 3 x ΔtTQ (as opposed to only the rise time as used in ELM analysis, Loarte/Federici)

Melting/ablation factor = ΔW / A / (ΔtTQdis)1/2 OR ΔT = ΔW x (2/k) x (α/π)1/2 / A / (ΔtTQ

dis)1/2 for square wave (Tillack)

Divertor energy flux = 3.5-35 MJ/m2, over 1.5-2.5 ms, giving 41-530 MW/m2-s1/2

FW(cond/conv) energy flux = 1.8-3.2 MJ/m2, over 1.5-2.5 ms, giving 21-48 MW/m2-s1/2

FW(radiation) energy flux = 0-0.75 MJ/m2 (OB) and 0-0.34 MJ/m2 (IB), assume 2 ms, giving ~ 16.8 MW/m2-s1/2 (OB) and ~ 7.6 MW/m2-s1/2 (IB)

>40 MW/m2-s1/2 begin melting of W surface

Plasma current quench phase• The current quench phase is initiated by the

thermal quench, when the plasma temperature drops to very low values

• Fastest Ip quench time, ~ 1.8 ms/m2 (from 100%-0% Ip), multiply this by plasma cross-sectional area πa2κ

– For ARIES with a = 1.38 m and κ=2.15, this is ~ 25 ms for a linear Ip drop

– OR about ~12 ms (about ½ the linear time) for an exponential Ip drop

– This is also the timescale for conducted/convected/radiated power to PFCs

• The current quench can turn into a runaway electron discharge before actually getting to 0 MA….we will discuss this later

Tokamak disruption database

During the current quench the magnetic energy in the plasma is mostly radiated away to the first wall

The ohmic dissipation of the plasma current is very strong, particularly at low Te……ηj2, where η~ 1/Te3/2

Low temperature plasmas are very good radiators

Radiated power levels are about 40-90% of the available magnetic energy…..1/2LintIp2, where Lint = μoRli/2….peaking factor in this phase is 1.5-2

For ARIES Wmag ~ 125 MJ (compared to ITER’s 350 MJ)

Some of the magnetic energy is going to end up generating eddy currents in surrounding structures

JET data

Some energy can also end up as conducted or convected power to the FW

No runaway electrons

Final radiated power loss after runaway electrons

Runaway electron current quenches change the power deposition split

There is usually some drop in Ip during the current quench before runaway electrons are generated, here ~50% of the magnetic energy could be released

The termination after the runaway current releases about 10-25% more of the magnetic energy as radiation

The remaining magnetic energy is released as some combination of 1)runaway electron impact (their kinetic energy)2)convection/conduction to the FW3)eddy currents induced in structures

Thermal Ip

Runaway Ip

Thermal Ip

Try some numbers for the current quench

ARIES magnetic energy is Wmag~ 125 MJ

Radiated power levels, with no runaway electrons, range from 40-90% give 50-113 MJ, assume 20% inboard and 80% outboard

Assume remainder is cond/conv to FW (outboard only), 12-75 MJ

FW intercepting area for radiated and cond/conv power = 157 / 2 (peaking) inboard, 287 / 2 (peaking) outboard, giving 79 m2 (IB) and 144 m2 (OB)

Time scale is ~ 12-25 ms

Energy densities are radiation < 0.68 MJ/m2 (OB), < 0.28 MJ/m2 (IB)Energy density for FW con/conv < 0.52 MJ/m2

These do not lead to significant loads compared to thermal quench

Runaway electrons can be a problem!

Runaway electrons energy deposition

JET IR measurements

Runaway electron impacts

We need to know the runaway current, estimate from Rosenbluth et al.

Then we can estimate the magnetic energy in the runaway current phase, which is dominated by the runaway current in spite of a residual thermal plasma current

In JET it is estimated that 20-60% of the runaway phase magnetic energy ends up as runaway kinetic energy

The energy deposited on the FW is expected to scale as Ip,runaway

2

Runaway electrons are lost to the FW often in a series of bursts, although single bursts have been seen

Still trying to establish the estimate for this….

Halo currents, flow from the cold plasma region into conducting structures making a poloidal circuit

(jpolxBtor forces)Halo currents emerge in the later part of the current quench

These are currents which form in the regions between the main plasma and the walls, the plasma is actually sharing current with this region because they are both low Te

Halo currents follow field lines and impact surrounding structures

the maximum product Ihalo/Ip x TPF toroidal peaking factor is taken to be 0.5-0.7, although latest data is suggesting the lower values