Electron mass without B-field: best precision?

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Roberto Pavani
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TL;DR
What is the most precise determination of the electron mass (or ##e/m_e##) that does not rely on a magnetic field?
The CODATA value of ##e/m_e## comes from Penning-trap cyclotron frequency measurements (strong ##B## field). Are there any competitive determinations of the same ratio ##e/m_e## using purely electric methods (no ##B##)? For instance from LINAC kinematics or Duane-Hunt bremsstrahlung? The papers I found have precisions of only 2–10%. Is there anything better?
 
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Linacs need to know that ratio to work, but they might not measure and publish that ratio as we already have way more precise measurements elsewhere.

In principle you can combine a direct charge measurement (-> Millikan) with spectroscopy of hydrogen (dominated by electric fields) to find the ratio.
 
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Thank you mfb. The idea of combining a direct charge measurement with hydrogen spectroscopy is a useful pointer. I'll look into what precision that route can achieve independently of ##B##-field methods.
 

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