# Presentation: 468360

## Beam Chamber Transport Requirements for

_**Beam Chamber Transport Requirements for**_
_**Flibe Vapor Pressure and Aerosol Conditions**_

**   **

**Craig Olson    **

**Sandia**

** ****National Laboratories, Albuquerque, NM**

**    **

**    ****Dale Welch     **

**Mission Research Corporation, Albuquerque, NM**

**    ****Dave Rose     **

** **

** **

**Mission Research Corporation, Albuquerque, NM**

**    ****Marlene Rosenberg  **

** **

** **

**University of California, San Diego, CA**

**                                              **

**ARIES Meeting**

**                            ****Princeton Plasma Physics Laboratory**

**                                          **

**   **

**  ****Princeton, NJ**

**                                         **

**  **

** ****October 2-4, 2002**

**Simon Yu       ****Lawrence Berkeley National Laboratory, Berkeley, CA **

##                                                               Outline

_**Motivation**_
**       ****transport modes**
**       ****effects of increasing line charge density**
_**Aerosol effects on ballistic transport**_
**       ********E/********x**
**       ****scattering**
**       ****stripping**
**       ****charged droplet effects**
**       ****micro-breakdown**
**       ****plasma-like effects**
_**Net effect of aerosols**_
**       ****integrated line density  **
**       ****effects on ballistic, channel, self-pinched transport**

## Neutralized Ballistic (mainline)

**Neutralized Ballistic (mainline)**

**Pinch modes (backup)**

## Aerosols may affect neutralized ballistic transport withthick liquid walls (the mainline approach for HIF)

-     (Per Peterson HIF2002 Invited Talk)

- Multiple beams converge onto one side of target, and Flibe jets for thick liquid wall chamber

## Slide 5

## A Series of Scaled Experiments at LBNL will address science issues of HIF

**         ****Concept: keep perveance K at driver-scale, and progressively increase ******
_**FFSE (Final Focus Scaled Experiment)                   **__***electron neutralization***_***        *****Completed**
**     ****160 keV Cs****+****,  95 - 400 ********A,       K = 1-4 x 10****-5****,     ******** = 2-8 x 10****-4**** ********C/m**
_**NTX (Neutralized Transport Experiment)   **__***neutralized ballistic transport***_**        ****Being set up**
**     ****400 keV K****+****,  75 mA,                 K ******** 10****-3****,              ********  ******** 0.05 ********C/m**
_**HCX (High Current Experiment)        **__***quadrupole transport in accelerator***_**       ****Underway**
**      ****1.8 MeV K****+****,  0.8 A                   K ******** 10****-3****,              ********  ******** 0.2 ********C/m**
_**IBX (Integrated Beam Experiment)**__***          first integrated system/bunching***_**       ****Proposed**
**      ****10-20 MeV K****+****,  10 A (final)    K ******** 10****-3****,              ********final**** ******** 1-2 ********C/m**
_**IRE (Integrated Research Experiment)        **__*** integrated system/heat matter***_***      *****Future**
**      ****200 MeV K****+****,  500A (final)      K ******** 7.5 x 10****-4****,     ********final**** ******** 17 ********C/m       **
**      **

## Several quantities scale with the line charge density 

**Beam potential:                            ********0**** = qI****p****/(********c) = ******
**Electric field at beam edge:         E****0**** = 2********0****/r****b**** = 2********/r****b**
**Current (electric):                        I****e**** = ********c**
**Magnetic field at beam edge:      B****0**** = 2I****e****/(cr****b****) = 2********/r****b**
**Time scale for electron motion:   ******** = 2R/(********e****c)  where (1/2)m****e********e****2****c****2**** = e********0****,   so ******** ******** ********-1/2**
**Beam density:                                n****b**** = ********/(********r****b****2****qe)**
**Beam plasma frequency:              ********bi**** = [4********n****b****qe****2****/(AM****p****)]****1/2  ******** ********1/2**
**Beam cyclotron frequency:           ********ci**** = qB/(AM****p****c)   ******** ******

**Example:  FFSE,    ******** ******** 8x10****-4**** ********C/m,    e********0**** ******** 8 eV,           E****0**** ******** 16 V/cm (for r****b**** = 1 cm)**
**                  ****Driver,   ******** ******** 80 ********C/m,          e********0**** ******** 0.8 MeV,    E****0**** ******** 1.6 MV/cm (for r****b**** = 1 cm)**

-  **Electron motion, non-local ionization, beam pinching, ********bi****, ********ci****, etc., increase with ******
** ****Need to study possible aerosol effects as ******** increases toward driver scale**

## Aerosol effects for neutralized ballistic transport 

_**Aerosol effects for neutralized ballistic**__** transport **_

- •

_****_

_**E/**_

_****_

_**x**_

**       **

**      **

** ****find aerosol limit for 10% energy loss**

- •

_**Scattering **_

**     ****assume **

**emittance **

**dominated spot**

**                                ****find limit for 10% increase in spot area (5% in radius)**

- •

_**Stripping  **_

**     ****find limit for onset**

- •

_**Charged droplets**_

**        ****charging processes**

**                                              ****role of ion beam in charging**

**                                              ****max **

****

** ****that droplet can attain**

**                                              ****simple deflection due to E**

- •

_**Micro-breakdown**_

**       ****fine mist, beam E leads to breakdown**

**                                              ****beam induced ionization of aerosol**

- •

_**Plasma-like effects of “charged aerosol”**_

**       **

**Debye**

**-like effects**

**                                              ****dusty plasma effects**

**          ****plasma waves, etc.**

## Slide 9

## Slide 10

## Slide 11

## Scattering limit

_**Scattering limit**_

**Multiple small-angle scattering:**

**  **

****

**rms**

** **

**= [**

****

**2**

****

**]**

**1/2**

**   ****where **

**       **

****

** **

****

**2**

** **

****

**  ****=  2**

****

**nL**

**[2qZe**

**2**

**/(Mv**

**2**

**]**

**2**

** **

**ln **

**[**

**b**

**max**

**/**

**b**

**min**

**]**

**                      ****incident beam ion:  +**

**qe**

**, M,  v**

**                      ****background medium:  n(atom density), Z charge on nucleus**

**Limit when   **

****

**rms**

** **

** ****=  [(1/2)**

****

**r**

**s**

**]/[(1/2)L]   where r**

**x**

** ****= spot radius**

**Therefore:**

**n**

**equivalent**

**  **

**=  [(**

****

**r**

**s**

**Mv**

**2**

**)/(L2qZe**

**2**

**)]**

**2**

**(2**

****

**L **

***ln***

**[  ])**

**-1**

**For:   4 **

**GeV Pb**

**,  L = 500 cm,  **

****

** ****= 0.1,  Z = 3, **

***ln***

**[  ] = 5,  r****s****=0.2 cm ;**

**           **

**n**

**equivalent**

** **

** ****=  1.06 x 10**

**18**

** ****cm**

**-3            **

**for q = +1**

**                               ****1.06 x 10**

**16**

** ****cm**

**-3**

**        ****for q = +10**

**                               ****1.58 x 10**

**14**

** ****cm**

**-3**

**        ****for q = +82**

## Stripping limit

_**Stripping limit**_

**Use a pressure of 1 **

**mTorr **

**to represent onset of damaging stripping effects**

**Then:**

**n**

- equivalent

**=  3.6 x 10**

**13**

** ****cm**

**-3**

**(based on LSP simulations of Welch and Rose)**

##                   Charges on aerosol droplets (“initial conditions”)

_**Example:**_** H.E. Hesketh, **_**Fine Particles in Gaseous Media**_** (Lewis Pub., 1986) p.10, p.74.**
**     “****As aerosols, fine particles can have no charge, a positive charge, or a negative charge”**
**     “****Most particles larger than 1 ********m in diameter have charge +1 as a result of diffusion charging”**
**       ****Maximum possible charge (limited by air breakdown) is about +5 for a 0.1 ********m particle**
**                   ****( i.e.,  Q/M ******** 10****-7**** e/M****p**** )**
_**Example:**_** E.C. Whipple, “Potentials of Surfaces in Space,” Rep. Prog. Phys. **_**44**_**, 1197-1250 (1981).**
**     “****Potentials of some tens of kV occur on objects in the solar system”**
**     “****Lack of hard data on charging of natural objects”**
_**Example:**_**  V.W. Chow, D.A. Mendis, M. Rosenberg, “Role of Grain Size and Particle Velocity  **
**    ****Distribution in Secondary Electron Emission in Space Plasmas,” J.G.R. **_**98**_**, 19,065-19076 (1993).**
**        “****By virtue of being generally immersed in a plasma environment, cosmic dust is necessarily charged”**
**        “****We find that for thermal energies that are expected in several cosmic regions, grains of different   **
**          ****sizes can have opposite charge, the smaller ones being positive while the larger ones are negative”**

** ****Charge may be + or -**
** ****Net charge to mass ratio is very small **
** ****Net potential is very small**

##            HIF beam injection through charged aerosol droplet

**           ****LSP simulation results (see following talk by Rose et al.)**

- D

**HIF beam ******

**Net  e******** ******** kT****e**** ******** 10 eV **

**aerosol droplet may be initially charged, radius used is 1 ********m**
**ion beam ionizes droplet and quickly forms plasma (******** 10****16****/cm****3****,  ******** 10 eV)**
**plasma shields charged droplet and limits net potential to e********  ******** kT****e**** ******** 10 eV**
**Debye sheath:  ********D**** ******** v****e****/********pe**** ******** 0.2 ********m**
**                          ****E  ******** ********/********D**** ******** (10 V)/(0.2 ********m) ******** 5x10****5**** V/cm, but only over 0.2 ********m**
**                          ****maximum deflection of ion in sheath is negligible compared to r****s****/L**
**                          ********D****  ******** r****droplet****  **
_**therefore, HIF beam deflection effects by “charged droplet deflection” are negligible**_

**Droplet causes usual losses by ********E/********x, scattering, and stripping**
**Integrated line density of aerosol droplets determines net effects**

- droplet

## Possibility of micro-breakdown of fine aerosol mist

**droplets inside the HIF beam quickly form plasmas **
**droplets outside the HIF beam could be subject to net beam fields**
**beam must be well-neutralized to hit target (f****e**** ******** 0.98),**
**so net potential and E****r**** of beam must be ********  (0.02)(bare beam values)**
**net value  for an HIF driver beam would be e******** ******** 16 keV**
**net minimum potential is given by (1/2)m****e****V****i****2**** ******** 10 keV**
**are these potential large enough to cause mist breakdown to nearby**
**      ****surfaces?**
**if this could occur, it would try to draw in electrons radially, but would **
**      ****not reduce the potential substantially**
**only potential damaging effect might be if nearby boundary is not    **
**     ****symmetric**

**Effects appear to be negligible **

##       Plasma-like effects of charged aerosol particles

**behaves as a separate plasma species**
**charge/mass ratio is very low, so plasma frequency is very low**
**Debye shielding could occur (e.g., outside beam envelope) but**
**       ****with little effect on the beam**
**plasma waves and instabilities could occur, but the time scale    **
**       ****would be very long compared to the beam pulse length**
_**Example:**_** M. Rosenberg, “Ion-Dust Streaming Instability in **
**    ****Processing Plasmas,”  J. Vac. Soc. Technol. A **_**14**_**, 631 (1996);**
**    ****nominal parameters - dust radius 0.3 ********m, density 10****6****/cm****3****,**
**    ****Q ******** 1000, dust T******** 0.05 eV   ********  ********p,dust**** ******** 4x10****3**** s****-1**** (extremely**
**    ****slow)**_** **_

**Plasma-like effects of aerosols appear to be negligible for HIF**

## Examples of n

_**Examples of n**_

_**aerosol**_

_**r**__**3**_

_** **__**for ballistic transport**_

** ****Recall: **

**       **

**n**

**aerosol**

** ****r**

**3**

**  ****=  [3/(4**

****

**)]**

** ****n**

**equivalent**

** ****/ **

**n**

**liquid**

**    **

**Use:             **

**n**

**liquid**

** **

** ****=  10**

**22**

** ****cm**

**-3**

**    **

**Then:           **

**n**

**aerosol **

**r**

**3**

**  ****=  1.0 x 10**

**-3**

**      ****for  **

****

**E/**

****

**x limit for q = +10**

**                        ****n**

**aerosol**

**r**

**3**

**  ****=   0.25 x 10**

**-6   **

**  ****for  scattering limit for q = +10**

**                        ****n**

**aerosol**

**r**

**3**

**  ****=   0.86 x 10**

**-9**

**    ****for stripping**

**   **_**Worst case is for stripping**_

**   ****Example (use **

**n**

**aerosol**

** **

**r**

**3**

** ****= 1 x 10**

**-9**

** ****):        **

**n**

**aerosol**

** **

**(cm**

**-3**

**)     r (micron)**

**  ****aerosol charge effects, micro-breakdown effects, plasma effects negligible**

##         Aerosol effects on neutralized ballistic transport

**            ****n****aerosol**** r****aerosol****3    **** = 1x10****-9**
**    **

**Stripping is dominant limit**
**Integrated line density equivalent to 1 mTorr**

##            Aerosol effects on channel transport

**Start with 1-10 Torr, and fully stripped beam**
******E/********x limit is n****equivalent**** = 6.2 x 10****17**** cm****-3**
**scattering limit (for ******** ******** 0.1) is n****equivalent**** = 3.95 x 10****16**** cm****-3**
**      ****n****aerosol ****r****aerosol****3****  ******** 1 x 10****-6**

**Scattering is dominant limit**
**Integrated line density equivalent to ******** 1 Torr**

##            Aerosol effects on self-pinched transport

**Start with 1-100 mTorr, and fully stripped beam**
******E/********x limit is n****equivalent**** = 6.2 x 10****17**** cm****-3**
**scattering limit (for ******** ******** 0.1) is n****equivalent**** = 3.95 x 10****16**** cm****-3**
**BUT, self-pinched process will require n****equivalent **** ******** 3.6 x 10****15**** cm****-3**
**      ****n****aerosol ****r****aerosol****3****  ******** 1 x 10****-7**

**Self-pinched process is dominant limit**
**Integrated line density equivalent to ******** 100 mTorr**

## Slide 22

##   Conclusions for Aerosol Effects on HIF Transport

_**neutralized ballistic:**_**  most stringent**
**                                     ****stripping sets limit**
**                                     ****integrated line density     **
**                                        ****equivalent to 1 mTorr**
_**channel transport:**_**  most forgiving**
**                                  ****scattering sets limit**
**                                  ****integrated line density **
**                                       ****equivalent to 1 Torr**
_**self-pinched transport:**_**  in between**
**                                         ****self-pinch sets limit**
**                                         ****integrated line density **
**                                              ****equivalent to 100 mTorr**

##                                         What needs to be done

**1.  **_**What needs to be done to complete this work?**_
**     ****Write up**
**     ****Determine if expected aerosol distribution is good enough**
**     ****Fix it if necessary**
**2.  **_**What can be done by the ARIES team (or you) to address these issues?**_
**     ****Self-pinched transport theory (analytic envelope, LSP)**
**     ****Determine expected aerosol distribution**
**3.  **_**What modeling/experimental work can be done to resolve these issues?**_
**     ****Ballistic transport experiments: NTX + metal arc source to make **
**                                                                         ****Al micro-particles**
**                                                            ****IBX + aerosols**
**     ****Pinched mode transport experiments:  Need high current!**
**                                         ****Not planned until IRE**
**                                         ****BUT, maybe  high-Z ion diode or Mercury at NRL**