1. Imperial College London 1 3. Beam extraction 3. Extraction of particle beams 3.1 The space charge limit and Child-Langmuirs law 3.2 External and internal fields in the extractor, laminar flow and pierce angle 3.3 The beam emittance, the acceptance of the extraction system and the conservation of phase space

2. Imperial College London 2 The extraction of particle beams The plasma generator and the extraction systems are defining : The extracted beam current The quality of the particle beam (emittance) Space charge forces in the extraction system and plasma properties of the source limit the beam current.

3. Imperial College London 3 The space charge limit and Child-Langmuir law anodecathode 0 +Ze z=d =-V 0 dz z=0 =0 (Poisson)

4. Imperial College London 4 The space charge limit and Child-Langmuir law

5. Imperial College London 5 Current limits given by the Child-Langmuir law The total current extractable from an ion source is given by : The area covered by the extraction aperture (~ d 2 ) Extraction voltage (U 3/2 ) Mass of particles (1/m) 1/2 Charge state ( ) 1/2 The distance between the electrodes (d 2 ) Under the assumption that the particle source is able to produce this current. For electron sources this is usually valid, for ion sources in general not !

6. Imperial College London 6 The Pierce method for the design of the extraction electrodes 1 anode 0d x z=0 =0 cathode z=d =V 0 z unbalanced space charge forces

7. Imperial College London 7 The Pierce method for the design of the extraction electrodes 2 anode 0d x z=0 =0 cathode z=d =V 0 z Individually biased electrodes to fulfil border condition

8. Imperial College London 8 The Pierce method for the design of the extraction electrodes 3 anode 0d x z=0 =0 cathode z=d =V 0 z

9. Imperial College London 9 The Pierce method for the design of the extraction electrodes 4 anode 0d z=0 =0 cathode z=d =V 0 z x

10. Imperial College London 10 Beam extraction, high voltage break down limit and aspect ratio Break down law: maximum current density for aspect ratio of :

11. Imperial College London 11 Phase space distribution of a particle beam

12. Imperial College London 12 The beam emittance, the phase space ellipse and the twist parameters x F= single trajectory z x x envelope acceptance

13. Imperial College London 13 Phase space distribution and beam emittance

14. Imperial College London 14 Conservation of phase space x x x x x x x x focusing Drift

15. Imperial College London 15 Influence of emittance on focal spot size

16. Imperial College London 16 Ion beam extraction from a plasma extraction system plasma plasma sheath plasmagenerator space charge The extractable current from an ion source is limited by : Space charge forces in the extraction region Plasma density in the source Production speed of ions in the plasma Diffusion speed of ions from the plasma into the plasma sheath Plasma sheath : While within the plasma the charges neutralize each other, the plasma itself is biased in respect to the walls to keep an equilibrium of losses between the fast electrons and slow ions. A thin boarder area (plasma sheath) separates the plasma from the outside by an electric field.

17. Imperial College London 17 Influence of particle density distribution at the extraction aperture on initial phase space distribution transversal current density profile phase space plasma

18. Imperial College London 18 Plasma density distribution at extraction aperture Experimental set up Experimental result Extraction aperture lens system aquisition analysis window In praxi the particle density at the extraction aperture is not homogeneous. This will lead to non linear space charge forces within the beam transport. Redistributions of the beam particles within the beam cause growth of the effective (RMS) beam emittance.

19. Imperial College London 19 The temperature of the source plasma, the potential depression in the plasma sheath and wall effects (losses of particles) are influencing the beam emittance. The transversal (and longitudinal) energy distribution of the beam ions is defined by the plasma temperature and the plasma potential (electric field in the plasma sheath) Losses of beam ions at the extraction electrode further reduces the number of ions to be extracted. Wall resolution

20. Imperial College London 20 Real extraction systems and the determination of beam formation radial space charge longitudinal edge particles Initial angle radial lens focus focus without space charge For real existing ion sources usually more than two extraction electrodes (here triode) are used to maximize beam current and to influence the beam emittance. To calculate beam formation self consistently numerical simulation codes like EGUN, IGUN, PBGUN or Cobra are used.

21. Imperial College London 21 Influence of beam current and aspect ration on beam emittance

22. Imperial College London 22 Numerical simulation of H - extraction and transport in the LEBT for SNS using PBGUN and comparison with measured data

23. Imperial College London 23 Numerical simulation of the extraction of a D + beam for IFMIF using IGUN and comparison with measured data