Characteristics and classification of plasmas PlasTEP trainings course and Summer school 2011 Warsaw/Szczecin Indrek Jõgi, University of Tartu Partfinanced by the European Union (European Regional Development Fund
Outline of the talk Introduction Characterization classification 1
Plasma and environment Environmental plasma Ionized gas with low temperatures but high electron energies Large amount of active species are produced radicals: O, OH, N etc. phenol CO 2 and H 2 O Other organic and inorganic species are neutralised similarly At some cost of energy 2
Plasma in the Universe Everything was plasma at the beginning of the Universe 95 or 99 % 3
Artificial plasma 4
Various plasma sources Different ways to generate plasma Corona discharge Dielectric barrier discharge Plasma torches Microwave plasmas Hollow cathode discharge Electron beams 5
Plasma: 4th state of the matter Solid 120 K Liquid Temperature Energy 0,01 ev 10 5 K 10eV 10 4 K 1eV Plasma 0,1 ev Gas 1200 K 10 3 K 0.1 ev 10 2 K 0.01 ev 12000 K 110 ev k B E = e0 T E = T/11600 6
Plasma: role of charge carriers F L = e 0 ( Ev B ) Occurrence of electrical conductivity Screening of electric fields Occurence of a multitude of oscillation and waves (Langmuir oscillations, ion acoustic oscillations, cyclotron oscillations, drift waves, surface waves etc.) Interaction with magnetic fields Formation of characteristic boundary sheaths due to the contact of plasmas with solid surfaces 7
Plasma: definition Neutral particles in gas interact only during collisions while charged particles in plasma interact through longrange forces Quasineutral gas of charged particles that exhibits collective behaviour How many charges do we need? Main criterias: Charged particles are close enough to affect large number of other particles Debye screening length is short compared to the dimensions of plasma itself. Plasmas are quasineutral Electron plasma frequency (plasma oscillations) is large compared to electron neutral collision frequency 8
Plasma: characteristics Neutrality and ionization degree Debye length, plasma frequency and plasma parameter Larmor radius and cyclotron frequency Conductivity Crosssections and mean free path Electron energy distribution 9
Ideal gas For ideal gas in thermal equilibrium the probability that velocity lays in the range dvaround velocity vis proportional to Maxwellian distribution: Rms. speed Average kinetic energy per particle electron at 300K: 10 5 m/s nitrogen at 300K: 500 m/s e 0= 1.60 10 19 C m e = 9.11 10 31 kg m p = 1.67 10 27 kg k B = 1.38 10 23 J/K ε 0 = 8.85 10 12 F/m c= 3.00 10 8 m/s 0.04 ev at 300K while 1.3 ev at 10 4 K Pressure is a measure of the density in thermal energy associated with the number of gas atoms per unit volume 10
Ionization degree All neutrals in a volume do not have to be ionized to obtain plasma Ionization degree the relative amount of charged particles in the total gas i = n e n 0 n e In atmosphere n 0 10 19 cm 3 n i 110 cm 3 Collisions with neutrals vs. the collective charge effects Environmental plasmas collisions dominate plasma density n e i 10 18 In environmental plasmas n i 10 10 to 10 15 cm 3 i 10 9 10 4 11
Plasma neutrality Neutral particle Sphere of influence Charged particle Q Q/r In most cases, the number of positive and negative charges will be roughly equal Quasineutral These charged particles will strongly intract with each other in plasma Collective motions Nonneutral plasmas: Ebeams, some magnetized plasmas 12
Debye length When there is charge imbalance in the plasma, it s influence will be neutralised in short distance E = e 0 (n i n e ) V m 10 9 8 6 4 In plasma the influence decays faster than in neutral gas 1/r vs. exp(r/λ D ) 2 0 Debye Coulomb 1 2 3 Space charge Debye length λ D = ε 0 k B T e e 02 n e In practical units: k B T e [ev], n e [cm 3 ] electron temperature electron density k λ D = 740 B T e cm n e 1 r/λ D 13
Debye length Inside the sphere defined by Debye length, one can observe charge imbalance while in larger sphere the charges are neutral Debye length k λ D = 740 B T e cm n e k B T e =4 ev n e =10 12 cm 3 λ D =14.8 µm k B T e =10 ev n e =10 15 cm 3 λ D =0.74 µm Debye screening length is short compared to the dimensions of plasma itself. Plasmas are quasineutral Electric field does not penetrate the plasma 14
Plasma parameter Charged particles are close enough to affect large number of other particles Plasma parameter inverse value of the number of charged particles inside the Debye sphere g = 1/N D λ D N D = n 4 πλ 3 D 3 k B T e n e N D T 3 n g<1 ideal plasma g>1 nonideal plasma 15
Plasma frequency When charges with opposite signs are slightly moved in plasma, there will be restoring force moving it back and the charges will oscillate with a certain frequency E Plasma frequency f 2 p = 1/2π e 02 n ε 0 m charge density mass of charges Electron mass smaller and thus they respond faster defining the plasma frequency f p = 1/2π e 02 n e ε 0 m e f p = 8980 n e Hz f p 0.1100 GHz 16
Plasma frequency Responsible for longitudinal electrical oscillations These oscillations are collisionless differently from acoustic waves where collisions between particles are necessary Determines the cut off frequency for electric fields to penetrate the plasma Determines one condition for the ideal plasma to occur When f c is the collision frequency f p 0.1100 GHz f p >> f c f c MHz to 100 GHz Electron plasma frequency (plasma oscillations) is large compared to electron neutral collision frequency 17
Larmor radius and cyclotron frequency Moving charge will experience Lorentz force in magnetic induction B v F L = e 0 v B F L It will start to move in circular motion perpenticularly to magnetic field Moving in parallel to magnetic field is not affected Composite motion is a helical spiral motion along the lines of magnetic induction Cyclotron frequency ω L = e 0B m Larmor radius r L = mv e 0 B 18
Larmor radius and cyclotron frequency Oppositely charged particles move along opposite direction v B v r L = mv e 0 B Radius is smaller for electrons ω L = e 0B m Cyclotron frequency is larger for electrons Magnetic field penertates the plasma Cyclotron frequency has to be larger than collision frequency for plasma to be magnetized E B Drift velocity v E = B 2 19
Electrical conductivity Action of electrical field E forces free electrons and ions of the plasma to gain drift velocities and generate an electric current E j = e 0 ( n e v e n i v i )= e 0 ( n e µ e n i µ i ) E Usually electrons determine the currents and µ e >>µ i n e n i Electrical conductivity σ = e 0 n e µ e σ = e 0 n e τ e /m e τ e mean free time of flight Weakly ionized plasmas τ e is independent on n e σ n e Fully ionized plasmas τ e 1/n e σ is not a function of n e 20
Ambipolar diffusion Diffusion will result in the expandsion of plasma Diffusion of electrons faster due to higher speed and smaller mass n Γ e = nµ e E D e n Γ i = nµ i E D i n electron flux ion flux ions Electric field due to different flux will counteract electron diffusion E E electrons x D a = µ i D e µ e D e µ i µ e n ambipolar diffusion The diffusion will be controlled by the inertia of ion collisions but increased by electron temperature There will be slightly more electrons at the boundary of plasma and more positive ions in the bulk of the plasma 21
Plasma sheaths Larger loss of charges at the boundaries with electrodes or other surfaces Electrons losses higher Positive charge in sheath Surface obtains negative potential in respect to plasma V E Electric field will prevent electrons to escape the plasma and will accelerate the ions Sheath thickness will be roughly 4λ D without applied voltage and potential drop in the range of kt e /e 0 Applying external voltage will change the thickness of plasma sheath 22
Formation of plasma Ionization Recombination Attachment Charge extraction from walls Diffusion to walls ionization has to balance the loss mechanisms Ionization e on O 2 Collisions by electrons, ions and neutrals photoionization There is certain threshold energy for ionization: U i 23
Formation of plasma Ionization at high temperatures Thermal energy of heavy particles becomes large enough for ionization Saha equation n i exp( ) n n i T T 3/2 n 3 10 27 n U i Ionization by electric fields Electric field accelerates charges and when they gain sufficient energy they will ionize the neutrals Most of environmental plasmas produced in this way Electrons mostly doing the work 24
Collisions Elastic collisions m Momentum is redistributed total kinetic energy is conserved Light particles, electrons, can not loose much of the energy M Redistributed energy < 2m M Inelastic collisions Momentum is redistributed Total kinetic energy transferred to internal energy Energy is lost for ionization, dissocitiation or excitation m M e A A 2e e A A * e e AB A B e Penning effect: excited atom or molecule has enough energy to ionize or dissociate another atom or molecule 25
Collision crosssections By the simplest approach the particles are treated as hard spheres without charge z x y Each atom presents a cross sectionobscuring electrons path σ=πr 2 volume xyz Number of target atoms is n xyz y x Viewed from the side of xy there is a distance λwhere the face xy is totally blocked by other particles: mean free path λ = 1/nσ around 0.1 µm at atmospheric pressures Collision frequency ν c = vnσ around 10 11 Hz at v ~ 10 5 m/s and atmospheric pressures In reality the particles not simple spheres and one has to take into account charge effects and the energy of the particles 26
Collision crosssections The probability for collisions depends on electron energy Inelastic collisions have certain thershold ionization (above 10 ev) excitation (about 0.110 ev) dissociation (about 110 ev) Cross sections decrease at higher energies Ar At high speed of electrons the time for interactions decreases The rate of ionizations, dissociations and excitations by electrons depend on electron energy which has a distribution 27
Electron energydistribution In environmental plasmas, electrons are carrying most of the energy and are main agents in the ionization, dissociation and exitation processes These processes depend strongly on electron energy distribution Maxwellian and Druyvesteyn Calculated Electron energy distribution becomes in equilibrium in timescales of 10 9 s 28
Nonequilibrium plasma Electron energy and average speed much higher than ions and neutrals Average electron energy 1 ev and average speed 10 6 m/s Average energy of surrounding gas 0.025 ev and average speed 1000 m/s Ionization, excitation and dissociation frequency can be obtained by integrating over energy distribution and cross sections Gas energy Electron energy Crosssection rate is additionally proportional to n e Energy not used in reactions is eventually lost Optimization of both the electron density and energy ev 29
Plasmachemistry The species with high energy have higher activity and shorter lifetime Plasma physics Plasma chemistry 10 12 10 10 Electron energy distribution 10 9 10 8 Ionization Dissociation Excitation Attachmenty 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10 1 Time, s Ion reactions Reactions of active species Radical reactions Diffusion Usually radical reactions in timescales of 10 6 to 10 s are most important in respect to removal of hazardous gases 30
Plasma: Classification Temperature low temperature plasmas (less than 2000K) high temperature plasmas (above 2000K) Thermodynamic equilibrium nonthermal or nonequilibrium plasmas T e >>T i T g thermal or equilibrium plasmas T e T i T g Pressure lowpressure plasmas <1 Pa moderate pressure plasmas 100 Pa atmospheric pressure plasmas Ionization degree weakly ionized plasmas 10 6 10 1 fully ionized plasmas 1 Frequency DC discharge pulsed DC (khz) RF discharge (MHz) Microwave discharge (GHz) Neutrality Magnetization magnetic plasmas nonmagnetic plasmas Dusty plasmas neutral nonneutral 31
Plasma: Classification Most often classified by electron temperature and plasma density 7 orders of magnitude by electron temperature 16 orders of magnitude by plasma density Environmental plasmas Electron temperature 110 ev Plasma density 10 10 10 14 cm 3 32