MZepf M.Zepf Queen s University Belfast

Transcription

1 Cone Guided dfast tignition MZepf M.Zepf Queen s University Belfast

2 Outline Inertial Confinement FusionConcepts The Fast Ignitor Concept Cone Guided Fast Ignition Electron Guiding

3 Inertial Confinement Fusion Basics Fusion Reaction basics what are we trying to achieve? compress fuel lto high h density and high h temperature what htare the requirements for gain

4 Fusion Energy Tritium 20 kev 3.5 MeV Helium Deuterium Neutron 20 kev 14 MeV The most promising reaction is based on two hydrogen isotopes, Deuterium (D) and Tritium (T). Reaction: D+T=He 4 [3.5 MeV]+n[14.1 MeV] Reaction energy: E DT =3.5 MeV MeV = 17.6 MeV Available for plasma heating: E CH =3.5 MeV

5 Requirements for Fusion Energy Gain Volume Rate: F=n D n T < V > Total Power: P DT =F*V*E DT Heating Power: P CH =F*V*3.5 MeV Plasma Temperature >10 kev (> 10 8 K) for DT Cross Section still very small. Other Reaction require far higher temperatures

6 We want to produce more energy than we put in the Lawson Criterium Hot plasma will loose energy Heat conduction (particles escaping) Radiation Characteristic time E =W/P LOSS W: Plasma energy; P loss : Energy loss rate Loss must be balanced by Fusion reaction for sustained energy production. F E CH ~ P loss F~ n 2 e > > Plasma must be confined to gain energy.

7 Using energy content ofdt plasma w=3 n e k B T F E CH = n D n T < V >E CH = 0.25 n e2 < V >E CH > 3 n e k B T / E n > (12 k B T )/ (E CH < >) n e e > (12 k B T )/ (E CH < v >) Minimum value at ~ 25 kev Lawson criterium: n e e > sm 3 = n e e > scm 3

8 Magnetic Confinement Fusion Small n e (~0.5-2 x cm -3 ) Long n e > many seconds. Achieving is a challenge Continuous burn possible

9 Inertial Confinement Fusion Driver Beam Blowoff Inwardly transported thermal energy Target heating A pulse of radiation (light or X rays) heats the surface of the pea sized fuel capsule Compression Thefuel is rapidly compressed by the rocket like blowoff of hot surface material Large n > cm 3 Very short <10 10 s Inherently pulsed energy Ignition When the fuel core reaches 20 times the density of lead it ignites at 10 8 K (10 kev) Burn Thermoclear ea burn quickly spreads through the compressed fuel yielding energy gain.

10 Inertial Confinement Fusion DT Confinement is purely inertial When a sound wave has crossed target there will be substantial decompression Sound crossing time R/c S with c s = (k B T m 1 I ) 1/2 E = R/3c s n E is typically experssed in terms of R (differs only by constants m i, c s E yp y p ( y y i, s A value of n E = corresponds to R=0.21

11 Burnup Fraction What is the total yield of an ICF burn? Nuclear Reaction Rate D,T density expressed in terms of initial density N 0 With Burnup fraction: Integration ti gives

12 Or confinement time Finally, With High Rresults in high burnup fractions R=3 corresponds to 33% burn up

13 Typical ICF fuel assembly Ablator (CH, Be) DT ICE DT DT Gas Pressure e Isobaric compression P fuel ~constant Centre: T~10 T10 kev, ~ g/cc =>P~Gbar Main Fuel: T~0.5 1 kev, ~30 50g/cc =>P~Gbar

14 Hotspot and alpha range Hotspot minimum scale is ultimately determined by p y y alpha particle range R~ is the effective minimum for central ignition

15 Typical Gain/Loss Diagramm

16 Instabilities IFAR and RT instability Mixing of fuel and hot spot This prevents ignition

17 The Fast Ignitor Concept The Fast Ignition Principle Scaling laws Physics Challenges Dli Delivering i the spark Energy electron propagation Laser propagation + Holeboring Alternatives to electron driven FI Alternatives to electron driven FI Proton/ion Shock Ignition

18 The Fast Ignition Principle Compression Dense Core Ignition Pulse <10ps Separate Compression and heating Burn Energy must be delivered before decompression FI <R/3c s <10ps Hence Fast

19 The Original Concept

20 Advantages and Additional Complication Much reduced energy requirements Due to Isochoric compression Less sensitive to instabilities No need to form central hot spot Analogy Central Ignition (conventional): Diesel Engine Spark Ignition (Fast Ignitor): Petrol Engine

21 Gain Curves 100 Target Gain Driver Energy (MJ) Much lower total laser Energy required for high target gain Much lower total laser Energy required for high target gain Target gains >50 are essential for Fusion Energy production

22 Isentropes Fuel Compressibility decreases with increasing entropy s= Q/ T In conventional ICF central hot spot has high entropy hot for constant pressure For Fast igntion the whole fuel can be on a low isentrope and have the same work (i.e. compression and heating) performed on it

23 Isobaric Compression Isochoric Compression Low Entropy High Entropy Low Entropy Low Entropy Press sure Isobaric Compression (Conventional ICF): High entropy main fuel increases cost of compression Trying to heat AND compress at same time. Isochoric Compression: Low Entropy > Low cost of compression Isochoric Compression: Low Entropy > Low cost of compression Requires separate energy input to achieve hot spot ~10keV

24 Gain in an ideal system Isochoric compression + separate Ignition is highly desirable Lower compression energy + substantially lower Ignition Energy => Higher Gain

25 Requirements for Ignition How much energy do we need to couple into a hot spot Energy to heat DT to 10keV: E 10 ~ Jkg 1 M=1.33 R 3 =( R) 3 / 2 for r= const => E 10 ~ 2 Very simple estimate Laser energy is modified by coupling efficiency => E L =E HS /. => E L ~10kJ sufficient? Simple Estimats

26 Hot spot size High densities imply very small hotspots R<20µm Electron beam must be very well confined Longitudinal energy deposition is critical!

27 Electron Range must be matched to R HS Binary range suggests E opt ~1MeV Additional Collective effects may allow highere Effective range is hard to model and hard to measure!

28 More Detailed Calculations increase energy needed S. Atzeni, Phys. Plas. 8, 3316 (1999) M Tabak et al Fus. Sci. Tech. (2006) Optimal ignition criteria: T = 12keV, R = 0.6 g/cm 2 Fast Ignition region E 2r DT z Z given by range R[g/cc]=0.6 E[MeV] For = 300 g/cm 3 assembly we need to deliver to the fuel: E = 18kJ in <2MeV> electrons P = 0.9 PW => t = 20ps I = 6.8x10 19 W/cm 2 => r = 20 m Coupling efficiency depends on: laser conversion to electrons energy spectrum of electrons collimation of electron transport cone tip to dense plasma separation Laser energy factor 4 6 larger than ignition energy Maximizing coupling efficiency at full scale is the overall design challenge in FI

29 This requires lasers at some enormous scale Initial estimates by Tabak in the 90s suggested lasers similar to todays would be enough Current estimates are order of magnitude larger and still somewhat uncertain

30 Simulations show that source distance and divergence have a large effect on coupling efficiency Coupling of electron source to ignition hot spot can be > 50% efficient for typical beam divergence and transport distance J Honrubia and J Meyer ter Vehn EPS Plasma Conf 2008

31 These requirments correspond to quite large lasers HIPER l i t dt h ~100kJ t 1 HIPER laser is expected to have ~100kJ at 1µm wavelength. This requires multiple phased beams

32 The original FI concept Max Tabak et al., Phys. Plasmas1,1626, (1994) 100 kj, 20 ps Laser holeboring and fast electron production are basis of original concept Optimal conditions

33 Why Holeboring? 300 ] Y [µm Ideal deposition i zone n CR X [µm] 300 Plasma has very long scalelength to implosion process (mm scale) Trying to hit ~20µm target Close coupling essential

34 Holeboring the principle Pondermotive pressure expells plasma radially F p ~ E 2. Very eyfast in underdense sepas plasmaa In overdense plasma progress slow and prone to instability. Velocity given by momentum conservation nmv 2 =I/c=P L v/c~n 1 M 1 I or about 2 and n=n cr

35 Original Concept the difficulties Wcm 2 hole boring in 1 mm scale sub critical density plasma C Ren FIW (2006) Channelling through mm scale plasma is possible to critical surface is possible Though not stable Still large outstanding problems Standoff distance of critical surface still large Long scalelength plasma results in ponderomotive energy scaling electrons get too hot No point design for Holeboring FI to date.

36 Electron spectra in long gradients are much hotter Long propagation through shallow gradients efficiently converts laser energy to very hot electrons! Channel would have to be very clean

37 Close coupling of energy deposition Holeboring can clear a void through long lengths of underdense plasma Butnot completely stable (e.g. Bullet without spin) Overdenseholeboring is slow (~few µm/ps) Instable Produces hot electrons for 10s of ps before Ignition pulse => reduces compression Hard to control electron spectrum (next section) =>Holeboring is a major risk factor for electron driven Fast Igintion

38 Hot Electron Production high efficiency is a MUST vxb Absorption drives Electrons into target talong axis. Becomes efficient for v~c Pondermotive scaling E pond =( 1)m 0 c 2, with =(1+a 02 ) 1/2 ~kt pond (Temperature ~ Free electron quiver energy) Typical Electronspectra: Exponential Spectrum with distribution f(e)=exp( E/kT pond )

39 Efficiency into electrons can be suitably high h PIC codes suggest 50 60% into hot electrons is possible Measurements by Ping (PRL 2008) show high absorption

40 OPTIMAL TEMPERATURE ~1 1.5 MeV A 0 ~3 4 (with hponderomotive Scaling)

41 How does this fit with our Assume ~ g/cc requirements so far? R~0.6 => R=12 20µm ~0.2 02(Electron production eff * Transport eff) Fraction of electron energy deposited in HS: 0.3 ~1.05µm => I 2 ~ Wcm 2 > a 0 ~30 E L =15/ =80 kj in 10ps into 10µm radius spot Electron Temperature >10 MeV MUCH TOO HOT Does this mean that FI doesn t work?

42 Transporting the energy with electrons We can calculate the mean energy of electrons very simply <E kin >=E L /N e =E L /Vn CR =E L /Ac n CR =16MeV for E L =10kJ, =10ps We cannot have beams denser than our interaction density For ponderomotive scaling n hot <n CR p g hot CR Can we increase the density?

43 Controlling the hot electron Temperature Ponderomotive scaling: E~I 2 is a free parameter, using shorter wavelengths i.e. harmonics of the laser is possible (if technically painful) Increase the laser interaction area an focus the electrons Concepts exist see later part Is it possible to increase the interaction density e.g. by using very steep plasma gradients Steep: e folding length L<<

44 Interaction with steep gradientsare are predicted d to reduce electron temperature A Kemp et al. PRL 2008 E hot a0 ( n c n p 1 ) 1/2 p Where =(1+a 02 ) 1/2

45 Measurements seem appear to agree Measurements by Hui Chen et al., APS DPP 05

46 Electron transport ~40 Divergence angle and stand off distance are critical for efficiency. i Coupling area must be less than R HS for optimal efficiency Electrons are injected into target at ~40 divergence.

47 Collective effects must be considered For I= Wcm 22, =1ps, r=15µm in an Al target We have E e beam =7J; I=24MA From this one can calculate: B=3200 MG and a total field Energy of 5kJ (>>E laser ) (Bell et al, PPCF 1997) Intense electron beams require a return current to propagate and set up self generated tde and B fields strong enough to influence propagation. Without such return currents the B field Energy would exceed the total laser energy for modest parameters

48 Hollowing vs focusing B t j j. I. First term B acts to push the fast electrons towards regions of higher fast electron density II. Second term pushes fast electrons towards higher resistivity. (Defocus for hot propagation axis) Two terms compete. Outcomedependson on experimental parameters

49 Divergence increases with Intensity Higher intensities make beam diverge more Surface (holeboring) and beam instabilities also important.

50 Summary of key parameters Hot spot requirmentsindicate a very large ps laser (~100kJ is required even for very god coupling to hot spot (~20 25%) 25%) To achieve this Standoff distance must be minimised. E beam < R HS, E beam propagation losses Propagation path in vacuum essential il Control of e beam production/temperature Avoid instabilities.

51 Cone Guided Ignition Cone Guided Ignition the principle Effect on compression How does a laser interact with a cone? Guiding electrons using material boundaries

52 Principle of Cone Guided Implosion Gold Cone Hollow Sphere Fast Ignition Pulse Compression Beams Compressed Core Vacuum Path to cone tip DefinedInterface interaction conditions can becontrolled Minimum standoff distance Spherical Implosion (alsmost) > high density core

53 Cone Shell Interaction Core does not stagnate on vertex due to asymmetry > core collides with ihcone tip Instabilities at interface? Scrape offbrings Hi Z material into core Shock Break out in cone

54 Wall Interaction S f L iibl Scrape of Layer visible little effect on regions far from foil Norreys et al. PoP 2000

55 Effect on Implosion Dynamics Compression to high and Ris possible with cone 70 80% of full spherical implosion Stand off distance from cone to vertex is a critical diamter > > prevent shock break out. Simulations from HIPER TDR

56 High R for gain possible with cone < R> DT =2.2 g cm 2 Laser Au cone 100 m S Hatchett et al 30 th Anom Abs Conf Maryland May 2000 S Hatchett et al. 30 th Anom. Abs. Conf. Maryland, May 2000 Radiation hydro simulations are well developed for ICF and allow hydro design optimization for FI

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58 Potential ti problems with cones relate lt to preplasma and hot electron propagation Both can limit the coupling efficiency Van Woerkom, PoP 2009

59 Cone Shell Interaction Cone wall typically high density (e.g. Au) to prevent shock breakout in cone Hi Z scrape of quenches burn due to radiation losses.

60 First Integrated Experiments Compression energy was adjusted to meet condition: heating laser energy ~ internal energy of core. This allows the effect of the Fast Ignitor beam to be seen more clearly. Target Parameters: Shell hll Radius r shell =250µm, Shell hllh thickness r shell =5 7µm Shell Material: deuterated Polystyrene (CD) Cone Material: Gold Distance cone tip to shell centre:50µm Compression laser: 9 beams Energy E comp =1.2kJ, Pulse duration t comp =1.2 ns Heating laser: One beam Energy: E heat =60 300J, Pulse duration: t heat =0.6ps

61 The image part with relationship ID rid2 was not found in the file. Core forms at the tip of the cone Time integrated X ray emission shows core forming at the tip of the cone. Emission from Cone walls Core emission Core density estimated to be ~60g/cc Good agreement with simulations given the illumination non uniformity. 250 m Acceleration Emission

62 (a) (b) (c) () Core self emission shows clear evidence of heating Heating pulse early not fully compressed Heating pulse correctly timed Heating pulse late Time relative to max compression (ps) a) c) show sequences of the core emission at 100 ps intervals. The effect of the heating pulse is clearly visible.

63 Relative timing is critical

64 Scaling with laser energy FI =30% FI =15% Experimental results show very high coupling fromlaser to hot spot

65 Experimental evidence for significantly enhanced e stopping? Classical e range Core r Classical electron range>> r core in the experiment Enhanced stopping OR Results of electrostatic electron confinement what happens for cores with r >> r HS?

66 LSP simulations suggest enhanced stopping Density e energy deposition Ion temperature Enhanced stopping due to Weibel instability in hot electron propagation. Static E field

67 Controlling Electron Flows with resistivity Gradients B t Recall j j. Spitzer Resistivity =10 4 Zln(Λ) T 3/2 Normally higher T on axis makes second term defocusing Atifii Artificial lz boundaries can reverse the sign of the gradient and make both terms collimating

68 Experimental Design Fe, Hi Z, Hi R Al, Low Z, Low R

69 Simulations show collimating fields GUIDED UNGUIDED Electron density B Z field Simulations by A. Robinson et al.

70 Collimation Clearly Visible FWHM Spot size in micro ometer y = 0.174x y = 0.177x Target thickness in micrometer Spot sizes measured from Cu K α Pinhole and HOPG data B Ramakrishna et al., (PRL submitted) 0.35 Guided Reference guide Reference

71 Good Confinement HOPG K αα Integrated signal K- signa al (a.u.) x Guided target with 25 um wire Reference 250 u Ref Guided target with 50 um wire Areal Density (g/cm 2 ) Data follows the simulation trend by Salzmann et al.,

72 Guiding could enhance cones Lo w Z substantially Hi Z Guiding through h longer walls Protection against shock break out. Collecting all electrons into Fuel Flexibility of Laser intensity Laser spotsize decoupled from Hotspot size Focusing into Fuel? Magnetic Lens

73 Alternatives Electron Fast Ignition Proton Fast Ignition

74 Conclusion ConeGuidedIgnition is a major step towards achieving Fast Ignition based on few ps electron bursts Proof of principle has been demonstrated Substantial Degreeof Physics demonstrated Some uncertainty without full scale experiments DT ice targets not yet demonstrated Particularly electron propagation and coupling to core Advantagesappearto appear to outweigh additionaleffort.