� ����������� �������������������� � ������������ !����"#�$�%��&�����'����(
)*���+"#����"-, �+./�0 1�&����($�2�������3 4�576�8�9��":���;)
��������������
������������������������� �
���!"���$#�%&��'�%(�$��) *+-,/. 02143656798;:/�:/:/�?A@(B�C6DFEF�@$�567/>�?A:/7/LM7/56�3PC6EF4YcDF36>�@�
Abstract
Spherical electrostatic probes are in wide use for the measurement of electric fields and
plasma density. This report concentrates on the measurement of fluctuations of these quan-
tities rather than background values. Potential problems with the technique include the
influence of density fluctuations on electric field measurements and vice versa, effects of
varying satellite potential, and non-linear rectification in the probe and satellite sheaths. To
study the actual importance of these and other possible effects, we simulate the response of
the probe-satellite system to various wave phenomena in the plasma by applying approxi-
mate analytical as well as numerical methods. We use a set of non-linear probe equations,
based on probe characteristics experimentally obtained in space, and therefore essentially in-
dependent of any specific probe theory. This approach is very useful since the probe theory
for magnetized plasmas is incomplete.
+
��� � �J���¥�����c���K�P�
EF DF36>�@$
�7/�F36
��� � �¥����� ��� �������2.1 Particle collection by spherical probes: Orbital motion limited or sheath
limited
? 1zCK��X8;7/�?^>4YP56EF�56M56EF
�7/�F36< +-Gf36xd}7/?F DF36>�@$�5656>�LzG@m(FD$mC67/567/>�?o>4Yyap15c214?fN�a�@�c�d}7/56EoCKF7/5K14@F:/�m14367/56EFLM7981[�-79C}CK8�14:/7/?Ff,
�7/?fN-7/?F56EF�? 7/?O56EF
EF�?f8;:/fC67/>�?56Ef145H[Z]\®14DFDF:/7/�3656�3}7/?fC65K14?f8;�3_�Yp>�F?fN 56Ef145[56EF
�7/�F36
d}EF�? a.YcP14?fNz56EFrde�?oC6D$
?��7/�F36< .��ed
�z� � �¥����� ������o�P�$� �����#��k�*����*�K�P� �K� ���� ��� ������ ��K�@c��� � ��� �3.1 Resistive coupling
JCKC6FLM7/?F14:/:I>�56EF(8�14:�?F>�?F:/7/?F4Y256EF�@$< 8;F36~m4Y�56EF<DF36>�@��D$�?
>4YR56EF
3.2 Capacitive coupling
EF�F?fN"56EF�@$
�7/�F36
�7/�F36
�7/�F36]36�365KC@(B +-&4I,92=$=B9v&('�)��z"$'!��'*921 �¨.��i�S43��NSz�(= e.(1 92'&�'�)��z"\'!��' 921D�¨.���B[3���14?fN��h&6.��]9��e&�=�A��¨.���+43$c , EF�5656>�L Df14?FxdPC=56EF�EF�? 56EF
�7/�F36�?«>4YPf36mCKC67/@F:/�8;>�?fC65636f8;514?o14:/LM>mCK5I8;>�3636�@$�F:9NX:/�?F�fC36�?F:/BM7¨Y�56EF4Y�:/7/?F
�7/�F36�?z8;B-8;:/>�5636>�?Ade1r~m�@fC6
79CPC6EF>xd}?A1�C56EF�L 1":/�56>w�?]8;F3636
�7/�F36
56EF�356EFoC6>o
�7/�F36�@fC6�?fC>4Y�C6>�:/7/5K1436B�d1�~m
�7/�F36�36@F7/5yimh�h�c2\�14?F�LF7/3�DF36>�@$
56>z8tEf14?F�7/?FACK1456�56�5�D�
HJ? UJ7/(7/?F �k~m>�:/5K14��@$
�7/�F36�?A>4Y�18m0Q LM
�U� � � ��� � ��P� � �K���M� ����K��5.1 Effects of sheath non-linearities on wave measurements
EF�@$(8tm�LM7/?f14?{5I?F>�?F:/7/?F(�@�w
56EF4Yyk
nl>x~mmC67/567/~m4Yjk
PYp36>�L 7/5KCJ< F7/:/7/@F367/FL ~x14:/F
�7/�F36< .�a-G m(7/LF:914567/>�?>4Y�36�?>4YJ56EF�:/5K14��31 E{B(D�>�56EF
@F7/D�>�:9143RC65636f8;56F36�@fC6�? 36�? 7/? 56EF
�7/�F36�@fC6
�7/�F36D$>�7/?{5KC7/?56EF�7/?{5145[.�,TaR OPb��(14?fNX8�14?F?F>�5I@�
1�C 7/5"79C ?F>�5"36�@��@$�56�L C67/LMDF:/< 1436�?fC679N-�?fC#a�< f14567/>�? a +�S�c2� �(k
SL1rB�@�<
56EF>�F�E{5"56>&@��564Y�:/7/LM7/56
:91436�< 14LMDF:/7/56fN-�56EF�365K14?(5_?F>�?F:/7/?F�L 56EF�@$
:/>xdY�36< F4YP56EF�@�
�7/�F36�? >4Y}f36
Yp36< F
7/LMDF:/BA56Ef145J56EF&1zD$>mCKC67/@F:/�F:9N @�mC C67/@F:/zfC6�@�
�e� ���P�� � � ��K�P�
EF�52@$�:/5K14��?(56�365K14?{5c56>_�364Y$?F>�?F:/7/?F
NF145K1F,�£ICKC6
� �����@������2��P?fN-3���@fCK�b�mC6(7/?F�:/@f1�8 � \�>xd Yp36< F
�[>x~(?F�?C�¥|=,-_e>mC6563 �>�Lv��14?fN __, OP>�:/@f1�8t �Mf36�@$�@fC6�?fC[>4Y�:/7/5K1436B�CK5636f8;56F36mC6(7/?F�:/@f1�8 ��02,kH, �J>x~{?FmC6563 �>�Lv� �, OP>�:/LM�36�36364Y{
\�1xYp3K14L @�>�79C6�?FLM>�36�¬F3636�:/:/�?«@{B DF36>�@$�?fN-�LM>�567/~m�3K8;4Y256EFw>�36�:/:/>(8t*� 3K14?fC6~m